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mrwulf
75ae21df06
- extract.sh: scoped Charon/Aeneas extraction of fields::fp (pow_vartime patched upstream to index loops — semantics-preserving, crate tests pass; sqrt/cmp/sum/random/... opaque, documented) - gen/: real transpiled model; subtle/CtOption hand-modeled (Choice := U8, CtOption := value × is_some), all other externals are axioms outside certificate cones - Proofs/PPallas: Lucas/Pratt primality certificate (reused — it was the one genuine piece of the previous attempt) - Proofs/Denote: Montgomery denotation ⟪a⟫ = feVal a · R⁻¹, Canon invariant - Proofs/HelperSpecs: adc/sbb/mac exact ℕ specs (step-registered) - Proofs/SubNegSpec: sub_spec (general two-case identity covering the t<2P reduction shape) and neg_spec, proven, no axioms Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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{"charon_version":"0.1.212","translated":{"crate_name":"pasta_curves","options":{"ullbc":false,"precise_drops":false,"skip_borrowck":false,"mir":null,"rustc_args":[],"targets":[],"monomorphize":false,"monomorphize_mut":null,"start_from":["crate::fields::fp"],"start_from_if_exists":[],"start_from_attribute":null,"start_from_pub":false,"include":[],"opaque":["crate::fields::fp::_::fmt","crate::fields::fp::_::pow_by_t_minus1_over2","crate::fields::fp::_::get_lower_32","crate::fields::fp::_::ZETA","crate::fields::fp::_::from_uniform_bytes","crate::fields::fp::_::sqrt","crate::fields::fp::_::sqrt_ratio","crate::fields::fp::_::random","crate::fields::fp::_::sum","crate::fields::fp::_::product","crate::fields::fp::_::cmp","crate::fields::fp::_::partial_cmp"],"exclude":[],"extract_opaque_bodies":false,"translate_all_methods":false,"duplicate_defaulted_methods":true,"lift_associated_types":["*"],"hide_marker_traits":true,"remove_adt_clauses":true,"hide_allocator":true,"remove_unused_self_clauses":true,"desugar_drops":false,"ops_to_function_calls":true,"index_to_function_calls":true,"treat_box_as_builtin":true,"raw_consts":false,"unsized_strings":false,"reconstruct_fallible_operations":true,"reconstruct_asserts":true,"unbind_item_vars":true,"print_original_ullbc":false,"print_ullbc":false,"print_built_llbc":false,"print_llbc":false,"dest_dir":null,"dest_file":"/home/oho/GitClone/Claude/FormalVerification/pasta-pallas-verified/verification/PallasFp.llbc","no_dedup_serialized_ast":false,"format":null,"no_serialize":false,"no_typecheck":false,"no_normalize":false,"abort_on_error":false,"error_on_warnings":false,"preset":"Aeneas"},"target_information":[{"key":"x86_64-unknown-linux-gnu","value":{"target_pointer_size":8,"is_little_endian":true}}],"files":[{"id":0,"name":{"Local":"src/fields.rs"},"crate_name":"pasta_curves","contents":"//! This module contains implementations for the two finite fields of the Pallas\n//! and Vesta curves.\n\nmod fp;\nmod fq;\n\npub use fp::*;\npub use fq::*;\n\n/// Converts 64-bit little-endian limbs to 32-bit little endian limbs.\n#[cfg(feature = \"gpu\")]\nfn u64_to_u32(limbs: &[u64]) -> alloc::vec::Vec<u32> {\n limbs\n .iter()\n .flat_map(|limb| [(limb & 0xFFFF_FFFF) as u32, (limb >> 32) as u32].into_iter())\n .collect()\n}\n\n#[cfg(feature = \"gpu\")]\n#[test]\nfn test_u64_to_u32() {\n use rand::{RngCore, SeedableRng};\n use rand_xorshift::XorShiftRng;\n\n let mut rng = XorShiftRng::from_seed([0; 16]);\n let u64_limbs: alloc::vec::Vec<u64> = (0..6).map(|_| rng.next_u64()).collect();\n let u32_limbs = crate::fields::u64_to_u32(&u64_limbs);\n\n let u64_le_bytes: alloc::vec::Vec<u8> = u64_limbs\n .iter()\n .flat_map(|limb| limb.to_le_bytes())\n .collect();\n let u32_le_bytes: alloc::vec::Vec<u8> = u32_limbs\n .iter()\n .flat_map(|limb| limb.to_le_bytes())\n .collect();\n\n assert_eq!(u64_le_bytes, u32_le_bytes);\n}\n"},{"id":1,"name":{"Local":"src/lib.rs"},"crate_name":"pasta_curves","contents":"//! Implementation of the Pallas / Vesta curve cycle.\n\n#![no_std]\n#![cfg_attr(docsrs, feature(doc_cfg))]\n#![allow(unknown_lints)]\n#![allow(clippy::op_ref, clippy::same_item_push, clippy::upper_case_acronyms)]\n#![deny(rustdoc::broken_intra_doc_links)]\n#![deny(missing_debug_implementations)]\n#![deny(missing_docs)]\n#![deny(unsafe_code)]\n\n#[cfg(feature = \"alloc\")]\nextern crate alloc;\n\n#[cfg(test)]\n#[macro_use]\nextern crate std;\n\n#[macro_use]\nmod macros;\nmod curves;\nmod fields;\n\npub mod arithmetic;\n#[cfg(feature = \"deferred\")]\n#[cfg_attr(docsrs, doc(cfg(feature = \"deferred\")))]\npub mod deferred;\npub mod pallas;\npub mod vesta;\n\n#[cfg(feature = \"alloc\")]\nmod hashtocurve;\n\n#[cfg(feature = \"serde\")]\nmod serde_impl;\n\npub use curves::*;\npub use fields::*;\n\npub extern crate group;\n\n#[cfg(feature = \"alloc\")]\n#[test]\nfn test_endo_consistency() {\n use crate::arithmetic::CurveExt;\n use group::{ff::WithSmallOrderMulGroup, Group};\n\n let a = pallas::Point::generator();\n assert_eq!(a * pallas::Scalar::ZETA, a.endo());\n let a = vesta::Point::generator();\n assert_eq!(a * vesta::Scalar::ZETA, a.endo());\n}\n"},{"id":2,"name":{"Local":"src/fields/fp.rs"},"crate_name":"pasta_curves","contents":"use core::fmt;\nuse core::ops::{Add, Mul, Neg, Sub};\n\nuse ff::{Field, FromUniformBytes, PrimeField, WithSmallOrderMulGroup};\nuse rand::RngCore;\nuse subtle::{Choice, ConditionallySelectable, ConstantTimeEq, CtOption};\n\n#[cfg(feature = \"sqrt-table\")]\nuse lazy_static::lazy_static;\n\n#[cfg(feature = \"bits\")]\nuse ff::{FieldBits, PrimeFieldBits};\n\nuse crate::arithmetic::{adc, mac, sbb, SqrtTableHelpers};\n#[cfg(feature = \"deferred\")]\nuse crate::deferred::{DeferredField, Product};\n\n#[cfg(feature = \"sqrt-table\")]\nuse crate::arithmetic::SqrtTables;\n\n/// This represents an element of $\\mathbb{F}_p$ where\n///\n/// `p = 0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001`\n///\n/// is the base field of the Pallas curve.\n// The internal representation of this type is four 64-bit unsigned\n// integers in little-endian order. `Fp` values are always in\n// Montgomery form; i.e., Fp(a) = aR mod p, with R = 2^256.\n#[derive(Clone, Copy, Eq)]\n#[repr(transparent)]\npub struct Fp(pub(crate) [u64; 4]);\n\nimpl fmt::Debug for Fp {\n fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {\n let tmp = self.to_repr();\n write!(f, \"0x\")?;\n for &b in tmp.iter().rev() {\n write!(f, \"{:02x}\", b)?;\n }\n Ok(())\n }\n}\n\nimpl From<bool> for Fp {\n fn from(bit: bool) -> Fp {\n if bit {\n Fp::one()\n } else {\n Fp::zero()\n }\n }\n}\n\nimpl From<u64> for Fp {\n fn from(val: u64) -> Fp {\n Fp([val, 0, 0, 0]) * R2\n }\n}\n\nimpl ConstantTimeEq for Fp {\n fn ct_eq(&self, other: &Self) -> Choice {\n self.0[0].ct_eq(&other.0[0])\n & self.0[1].ct_eq(&other.0[1])\n & self.0[2].ct_eq(&other.0[2])\n & self.0[3].ct_eq(&other.0[3])\n }\n}\n\nimpl PartialEq for Fp {\n #[inline]\n fn eq(&self, other: &Self) -> bool {\n self.ct_eq(other).unwrap_u8() == 1\n }\n}\n\nimpl core::cmp::Ord for Fp {\n fn cmp(&self, other: &Self) -> core::cmp::Ordering {\n let left = self.to_repr();\n let right = other.to_repr();\n left.iter()\n .zip(right.iter())\n .rev()\n .find_map(|(left_byte, right_byte)| match left_byte.cmp(right_byte) {\n core::cmp::Ordering::Equal => None,\n res => Some(res),\n })\n .unwrap_or(core::cmp::Ordering::Equal)\n }\n}\n\nimpl core::cmp::PartialOrd for Fp {\n fn partial_cmp(&self, other: &Self) -> Option<core::cmp::Ordering> {\n Some(self.cmp(other))\n }\n}\n\nimpl ConditionallySelectable for Fp {\n fn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self {\n Fp([\n u64::conditional_select(&a.0[0], &b.0[0], choice),\n u64::conditional_select(&a.0[1], &b.0[1], choice),\n u64::conditional_select(&a.0[2], &b.0[2], choice),\n u64::conditional_select(&a.0[3], &b.0[3], choice),\n ])\n }\n}\n\n/// Constant representing the modulus\n/// p = 0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001\nconst MODULUS: Fp = Fp([\n 0x992d30ed00000001,\n 0x224698fc094cf91b,\n 0x0000000000000000,\n 0x4000000000000000,\n]);\n\n/// The modulus as u32 limbs.\n#[cfg(not(target_pointer_width = \"64\"))]\nconst MODULUS_LIMBS_32: [u32; 8] = [\n 0x0000_0001,\n 0x992d_30ed,\n 0x094c_f91b,\n 0x2246_98fc,\n 0x0000_0000,\n 0x0000_0000,\n 0x0000_0000,\n 0x4000_0000,\n];\n\nimpl<'a> Neg for &'a Fp {\n type Output = Fp;\n\n #[inline]\n fn neg(self) -> Fp {\n self.neg()\n }\n}\n\nimpl Neg for Fp {\n type Output = Fp;\n\n #[inline]\n fn neg(self) -> Fp {\n -&self\n }\n}\n\nimpl<'a, 'b> Sub<&'b Fp> for &'a Fp {\n type Output = Fp;\n\n #[inline]\n fn sub(self, rhs: &'b Fp) -> Fp {\n self.sub(rhs)\n }\n}\n\nimpl<'a, 'b> Add<&'b Fp> for &'a Fp {\n type Output = Fp;\n\n #[inline]\n fn add(self, rhs: &'b Fp) -> Fp {\n self.add(rhs)\n }\n}\n\nimpl<'a, 'b> Mul<&'b Fp> for &'a Fp {\n type Output = Fp;\n\n #[inline]\n fn mul(self, rhs: &'b Fp) -> Fp {\n self.mul(rhs)\n }\n}\n\nimpl_binops_additive!(Fp, Fp);\nimpl_binops_multiplicative!(Fp, Fp);\n\nimpl<T: ::core::borrow::Borrow<Fp>> ::core::iter::Sum<T> for Fp {\n fn sum<I: Iterator<Item = T>>(iter: I) -> Self {\n iter.fold(Self::ZERO, |acc, item| acc + item.borrow())\n }\n}\n\nimpl<T: ::core::borrow::Borrow<Fp>> ::core::iter::Product<T> for Fp {\n fn product<I: Iterator<Item = T>>(iter: I) -> Self {\n iter.fold(Self::ONE, |acc, item| acc * item.borrow())\n }\n}\n\n/// INV = -(p^{-1} mod 2^64) mod 2^64\nconst INV: u64 = 0x992d30ecffffffff;\n\n/// R = 2^256 mod p\nconst R: Fp = Fp([\n 0x34786d38fffffffd,\n 0x992c350be41914ad,\n 0xffffffffffffffff,\n 0x3fffffffffffffff,\n]);\n\n/// R^2 = 2^512 mod p\nconst R2: Fp = Fp([\n 0x8c78ecb30000000f,\n 0xd7d30dbd8b0de0e7,\n 0x7797a99bc3c95d18,\n 0x096d41af7b9cb714,\n]);\n\n/// R^3 = 2^768 mod p\nconst R3: Fp = Fp([\n 0xf185a5993a9e10f9,\n 0xf6a68f3b6ac5b1d1,\n 0xdf8d1014353fd42c,\n 0x2ae309222d2d9910,\n]);\n\n/// `GENERATOR = 5 mod p` is a generator of the `p - 1` order multiplicative\n/// subgroup, or in other words a primitive root of the field.\nconst GENERATOR: Fp = Fp::from_raw([\n 0x0000_0000_0000_0005,\n 0x0000_0000_0000_0000,\n 0x0000_0000_0000_0000,\n 0x0000_0000_0000_0000,\n]);\n\nconst S: u32 = 32;\n\n/// GENERATOR^t where t * 2^s + 1 = p\n/// with t odd. In other words, this\n/// is a 2^s root of unity.\nconst ROOT_OF_UNITY: Fp = Fp::from_raw([\n 0xbdad6fabd87ea32f,\n 0xea322bf2b7bb7584,\n 0x362120830561f81a,\n 0x2bce74deac30ebda,\n]);\n\n/// GENERATOR^{2^s} where t * 2^s + 1 = p\n/// with t odd. In other words, this\n/// is a t root of unity.\nconst DELTA: Fp = Fp::from_raw([\n 0x6a6ccd20dd7b9ba2,\n 0xf5e4f3f13eee5636,\n 0xbd455b7112a5049d,\n 0x0a757d0f0006ab6c,\n]);\n\n/// `(t - 1) // 2` where t * 2^s + 1 = p with t odd.\n#[cfg(any(test, not(feature = \"sqrt-table\")))]\nconst T_MINUS1_OVER2: [u64; 4] = [\n 0x04a6_7c8d_cc96_9876,\n 0x0000_0000_1123_4c7e,\n 0x0000_0000_0000_0000,\n 0x0000_0000_2000_0000,\n];\n\nimpl Default for Fp {\n #[inline]\n fn default() -> Self {\n Self::zero()\n }\n}\n\nimpl Fp {\n /// Returns zero, the additive identity.\n #[inline]\n pub const fn zero() -> Fp {\n Fp([0, 0, 0, 0])\n }\n\n /// Returns one, the multiplicative identity.\n #[inline]\n pub const fn one() -> Fp {\n R\n }\n\n /// Doubles this field element.\n #[inline]\n pub const fn double(&self) -> Fp {\n // TODO: This can be achieved more efficiently with a bitshift.\n self.add(self)\n }\n\n fn from_u512(limbs: [u64; 8]) -> Fp {\n // We reduce an arbitrary 512-bit number by decomposing it into two 256-bit digits\n // with the higher bits multiplied by 2^256. Thus, we perform two reductions\n //\n // 1. the lower bits are multiplied by R^2, as normal\n // 2. the upper bits are multiplied by R^2 * 2^256 = R^3\n //\n // and computing their sum in the field. It remains to see that arbitrary 256-bit\n // numbers can be placed into Montgomery form safely using the reduction. The\n // reduction works so long as the product is less than R=2^256 multiplied by\n // the modulus. This holds because for any `c` smaller than the modulus, we have\n // that (2^256 - 1)*c is an acceptable product for the reduction. Therefore, the\n // reduction always works so long as `c` is in the field; in this case it is either the\n // constant `R2` or `R3`.\n let d0 = Fp([limbs[0], limbs[1], limbs[2], limbs[3]]);\n let d1 = Fp([limbs[4], limbs[5], limbs[6], limbs[7]]);\n // Convert to Montgomery form\n d0 * R2 + d1 * R3\n }\n\n /// Converts from an integer represented in little endian\n /// into its (congruent) `Fp` representation.\n pub const fn from_raw(val: [u64; 4]) -> Self {\n (&Fp(val)).mul(&R2)\n }\n\n /// Squares this element.\n #[cfg_attr(not(feature = \"uninline-portable\"), inline)]\n pub const fn square(&self) -> Fp {\n let u = self.square_unreduced();\n Fp::montgomery_reduce(u[0], u[1], u[2], u[3], u[4], u[5], u[6], u[7])\n }\n\n #[allow(clippy::too_many_arguments)]\n #[cfg_attr(not(feature = \"uninline-portable\"), inline(always))]\n const fn montgomery_reduce(\n r0: u64,\n r1: u64,\n r2: u64,\n r3: u64,\n r4: u64,\n r5: u64,\n r6: u64,\n r7: u64,\n ) -> Self {\n // The Montgomery reduction here is based on Algorithm 14.32 in\n // Handbook of Applied Cryptography\n // <http://cacr.uwaterloo.ca/hac/about/chap14.pdf>.\n\n let k = r0.wrapping_mul(INV);\n let (_, carry) = mac(r0, k, MODULUS.0[0], 0);\n let (r1, carry) = mac(r1, k, MODULUS.0[1], carry);\n let (r2, carry) = mac(r2, k, MODULUS.0[2], carry);\n let (r3, carry) = mac(r3, k, MODULUS.0[3], carry);\n let (r4, carry2) = adc(r4, 0, carry);\n\n let k = r1.wrapping_mul(INV);\n let (_, carry) = mac(r1, k, MODULUS.0[0], 0);\n let (r2, carry) = mac(r2, k, MODULUS.0[1], carry);\n let (r3, carry) = mac(r3, k, MODULUS.0[2], carry);\n let (r4, carry) = mac(r4, k, MODULUS.0[3], carry);\n let (r5, carry2) = adc(r5, carry2, carry);\n\n let k = r2.wrapping_mul(INV);\n let (_, carry) = mac(r2, k, MODULUS.0[0], 0);\n let (r3, carry) = mac(r3, k, MODULUS.0[1], carry);\n let (r4, carry) = mac(r4, k, MODULUS.0[2], carry);\n let (r5, carry) = mac(r5, k, MODULUS.0[3], carry);\n let (r6, carry2) = adc(r6, carry2, carry);\n\n let k = r3.wrapping_mul(INV);\n let (_, carry) = mac(r3, k, MODULUS.0[0], 0);\n let (r4, carry) = mac(r4, k, MODULUS.0[1], carry);\n let (r5, carry) = mac(r5, k, MODULUS.0[2], carry);\n let (r6, carry) = mac(r6, k, MODULUS.0[3], carry);\n let (r7, _) = adc(r7, carry2, carry);\n\n // Result may be within MODULUS of the correct value\n (&Fp([r4, r5, r6, r7])).sub(&MODULUS)\n }\n\n /// Multiplies `rhs` by `self`, returning the result.\n #[cfg_attr(not(feature = \"uninline-portable\"), inline)]\n pub const fn mul(&self, rhs: &Self) -> Self {\n let u = self.mul_unreduced(rhs);\n Fp::montgomery_reduce(u[0], u[1], u[2], u[3], u[4], u[5], u[6], u[7])\n }\n\n /// Subtracts `rhs` from `self`, returning the result.\n #[cfg_attr(not(feature = \"uninline-portable\"), inline)]\n pub const fn sub(&self, rhs: &Self) -> Self {\n let (d0, borrow) = sbb(self.0[0], rhs.0[0], 0);\n let (d1, borrow) = sbb(self.0[1], rhs.0[1], borrow);\n let (d2, borrow) = sbb(self.0[2], rhs.0[2], borrow);\n let (d3, borrow) = sbb(self.0[3], rhs.0[3], borrow);\n\n // If underflow occurred on the final limb, borrow = 0xfff...fff, otherwise\n // borrow = 0x000...000. Thus, we use it as a mask to conditionally add the modulus.\n let (d0, carry) = adc(d0, MODULUS.0[0] & borrow, 0);\n let (d1, carry) = adc(d1, MODULUS.0[1] & borrow, carry);\n let (d2, carry) = adc(d2, MODULUS.0[2] & borrow, carry);\n let (d3, _) = adc(d3, MODULUS.0[3] & borrow, carry);\n\n Fp([d0, d1, d2, d3])\n }\n\n /// Adds `rhs` to `self`, returning the result.\n #[cfg_attr(not(feature = \"uninline-portable\"), inline)]\n pub const fn add(&self, rhs: &Self) -> Self {\n let (d0, carry) = adc(self.0[0], rhs.0[0], 0);\n let (d1, carry) = adc(self.0[1], rhs.0[1], carry);\n let (d2, carry) = adc(self.0[2], rhs.0[2], carry);\n let (d3, _) = adc(self.0[3], rhs.0[3], carry);\n\n // Attempt to subtract the modulus, to ensure the value\n // is smaller than the modulus.\n (&Fp([d0, d1, d2, d3])).sub(&MODULUS)\n }\n\n /// Negates `self`.\n #[cfg_attr(not(feature = \"uninline-portable\"), inline)]\n pub const fn neg(&self) -> Self {\n // Subtract `self` from `MODULUS` to negate. Ignore the final\n // borrow because it cannot underflow; self is guaranteed to\n // be in the field.\n let (d0, borrow) = sbb(MODULUS.0[0], self.0[0], 0);\n let (d1, borrow) = sbb(MODULUS.0[1], self.0[1], borrow);\n let (d2, borrow) = sbb(MODULUS.0[2], self.0[2], borrow);\n let (d3, _) = sbb(MODULUS.0[3], self.0[3], borrow);\n\n // `tmp` could be `MODULUS` if `self` was zero. Create a mask that is\n // zero if `self` was zero, and `u64::max_value()` if self was nonzero.\n let mask = (((self.0[0] | self.0[1] | self.0[2] | self.0[3]) == 0) as u64).wrapping_sub(1);\n\n Fp([d0 & mask, d1 & mask, d2 & mask, d3 & mask])\n }\n\n /// Multiplies `rhs` by `self`, returning the unreduced 512-bit product.\n #[cfg_attr(not(feature = \"uninline-portable\"), inline)]\n pub(crate) const fn mul_unreduced(&self, rhs: &Self) -> [u64; 8] {\n // Schoolbook multiplication\n\n let (r0, carry) = mac(0, self.0[0], rhs.0[0], 0);\n let (r1, carry) = mac(0, self.0[0], rhs.0[1], carry);\n let (r2, carry) = mac(0, self.0[0], rhs.0[2], carry);\n let (r3, r4) = mac(0, self.0[0], rhs.0[3], carry);\n\n let (r1, carry) = mac(r1, self.0[1], rhs.0[0], 0);\n let (r2, carry) = mac(r2, self.0[1], rhs.0[1], carry);\n let (r3, carry) = mac(r3, self.0[1], rhs.0[2], carry);\n let (r4, r5) = mac(r4, self.0[1], rhs.0[3], carry);\n\n let (r2, carry) = mac(r2, self.0[2], rhs.0[0], 0);\n let (r3, carry) = mac(r3, self.0[2], rhs.0[1], carry);\n let (r4, carry) = mac(r4, self.0[2], rhs.0[2], carry);\n let (r5, r6) = mac(r5, self.0[2], rhs.0[3], carry);\n\n let (r3, carry) = mac(r3, self.0[3], rhs.0[0], 0);\n let (r4, carry) = mac(r4, self.0[3], rhs.0[1], carry);\n let (r5, carry) = mac(r5, self.0[3], rhs.0[2], carry);\n let (r6, r7) = mac(r6, self.0[3], rhs.0[3], carry);\n\n [r0, r1, r2, r3, r4, r5, r6, r7]\n }\n\n /// Squares this element, returning the unreduced 512-bit product.\n #[cfg_attr(not(feature = \"uninline-portable\"), inline)]\n pub(crate) const fn square_unreduced(&self) -> [u64; 8] {\n let (r1, carry) = mac(0, self.0[0], self.0[1], 0);\n let (r2, carry) = mac(0, self.0[0], self.0[2], carry);\n let (r3, r4) = mac(0, self.0[0], self.0[3], carry);\n\n let (r3, carry) = mac(r3, self.0[1], self.0[2], 0);\n let (r4, r5) = mac(r4, self.0[1], self.0[3], carry);\n\n let (r5, r6) = mac(r5, self.0[2], self.0[3], 0);\n\n let r7 = r6 >> 63;\n let r6 = (r6 << 1) | (r5 >> 63);\n let r5 = (r5 << 1) | (r4 >> 63);\n let r4 = (r4 << 1) | (r3 >> 63);\n let r3 = (r3 << 1) | (r2 >> 63);\n let r2 = (r2 << 1) | (r1 >> 63);\n let r1 = r1 << 1;\n\n let (r0, carry) = mac(0, self.0[0], self.0[0], 0);\n let (r1, carry) = adc(0, r1, carry);\n let (r2, carry) = mac(r2, self.0[1], self.0[1], carry);\n let (r3, carry) = adc(0, r3, carry);\n let (r4, carry) = mac(r4, self.0[2], self.0[2], carry);\n let (r5, carry) = adc(0, r5, carry);\n let (r6, carry) = mac(r6, self.0[3], self.0[3], carry);\n let (r7, _) = adc(0, r7, carry);\n\n [r0, r1, r2, r3, r4, r5, r6, r7]\n }\n}\n\n#[cfg(feature = \"deferred\")]\nimpl DeferredField for Fp {\n type Accumulator = Product<Fp>;\n\n #[cfg_attr(not(feature = \"uninline-portable\"), inline)]\n fn mul_accumulate(acc: &mut Self::Accumulator, a: &Fp, b: &Fp) {\n acc.accumulate(a.mul_unreduced(b));\n }\n\n #[cfg_attr(not(feature = \"uninline-portable\"), inline)]\n fn square_accumulate(acc: &mut Self::Accumulator, a: &Fp) {\n acc.accumulate(a.square_unreduced());\n }\n\n #[cfg_attr(not(feature = \"uninline-portable\"), inline)]\n fn reduce(acc: Self::Accumulator) -> Fp {\n /// 2^448 mod p (little-endian limbs).\n const B448: [u64; 4] = [\n 0x9b9858f294cf91ba,\n 0x8635bd2c4252b065,\n 0x496d41af7b9cb714,\n 0x1b4b3c4bfffffffc,\n ];\n let limbs = acc.partial_reduce(&B448, &R2.0);\n Fp::montgomery_reduce(\n limbs[0], limbs[1], limbs[2], limbs[3], limbs[4], limbs[5], limbs[6], limbs[7],\n )\n }\n}\n\nimpl From<Fp> for [u8; 32] {\n fn from(value: Fp) -> [u8; 32] {\n value.to_repr()\n }\n}\n\nimpl<'a> From<&'a Fp> for [u8; 32] {\n fn from(value: &'a Fp) -> [u8; 32] {\n value.to_repr()\n }\n}\n\nimpl ff::Field for Fp {\n const ZERO: Self = Self::zero();\n const ONE: Self = Self::one();\n\n fn random(mut rng: impl RngCore) -> Self {\n Self::from_u512([\n rng.next_u64(),\n rng.next_u64(),\n rng.next_u64(),\n rng.next_u64(),\n rng.next_u64(),\n rng.next_u64(),\n rng.next_u64(),\n rng.next_u64(),\n ])\n }\n\n fn double(&self) -> Self {\n self.double()\n }\n\n #[inline(always)]\n fn square(&self) -> Self {\n self.square()\n }\n\n fn sqrt_ratio(num: &Self, div: &Self) -> (Choice, Self) {\n #[cfg(feature = \"sqrt-table\")]\n {\n FP_TABLES.sqrt_ratio(num, div)\n }\n\n #[cfg(not(feature = \"sqrt-table\"))]\n ff::helpers::sqrt_ratio_generic(num, div)\n }\n\n #[cfg(feature = \"sqrt-table\")]\n fn sqrt_alt(&self) -> (Choice, Self) {\n FP_TABLES.sqrt_alt(self)\n }\n\n /// Computes the square root of this element, if it exists.\n fn sqrt(&self) -> CtOption<Self> {\n #[cfg(feature = \"sqrt-table\")]\n {\n let (is_square, res) = FP_TABLES.sqrt_alt(self);\n CtOption::new(res, is_square)\n }\n\n #[cfg(not(feature = \"sqrt-table\"))]\n ff::helpers::sqrt_tonelli_shanks(self, &T_MINUS1_OVER2)\n }\n\n /// Computes the multiplicative inverse of this element,\n /// failing if the element is zero.\n fn invert(&self) -> CtOption<Self> {\n let tmp = self.pow_vartime(&[\n 0x992d30ecffffffff,\n 0x224698fc094cf91b,\n 0x0,\n 0x4000000000000000,\n ]);\n\n CtOption::new(tmp, !self.ct_eq(&Self::zero()))\n }\n\n fn pow_vartime<S: AsRef<[u64]>>(&self, exp: S) -> Self {\n // PATCH (Aeneas compatibility): index-based loops instead of\n // `iter().rev()` / `(0..64).rev()` (double-ended range iterators have\n // no Aeneas model). Iteration order and arithmetic are IDENTICAL to\n // upstream: limbs from most- to least-significant, bits from high to\n // low, square-then-conditionally-multiply.\n let mut res = Self::one();\n let mut found_one = false;\n let exp = exp.as_ref();\n let mut j = exp.len();\n while j > 0 {\n j -= 1;\n let e = exp[j];\n let mut i = 64u32;\n while i > 0 {\n i -= 1;\n if found_one {\n res = res.square();\n }\n\n if ((e >> i) & 1) == 1 {\n found_one = true;\n res *= self;\n }\n }\n }\n res\n }\n}\n\nimpl ff::PrimeField for Fp {\n type Repr = [u8; 32];\n\n const MODULUS: &'static str =\n \"0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001\";\n const TWO_INV: Self = Fp::from_raw([\n 0xcc96987680000001,\n 0x11234c7e04a67c8d,\n 0x0000000000000000,\n 0x2000000000000000,\n ]);\n const NUM_BITS: u32 = 255;\n const CAPACITY: u32 = 254;\n const MULTIPLICATIVE_GENERATOR: Self = GENERATOR;\n const S: u32 = S;\n const ROOT_OF_UNITY: Self = ROOT_OF_UNITY;\n const ROOT_OF_UNITY_INV: Self = Fp::from_raw([\n 0xf0b87c7db2ce91f6,\n 0x84a0a1d8859f066f,\n 0xb4ed8e647196dad1,\n 0x2cd5282c53116b5c,\n ]);\n const DELTA: Self = DELTA;\n\n fn from_u128(v: u128) -> Self {\n Fp::from_raw([v as u64, (v >> 64) as u64, 0, 0])\n }\n\n fn from_repr(repr: Self::Repr) -> CtOption<Self> {\n let mut tmp = Fp([0, 0, 0, 0]);\n\n tmp.0[0] = u64::from_le_bytes(repr[0..8].try_into().unwrap());\n tmp.0[1] = u64::from_le_bytes(repr[8..16].try_into().unwrap());\n tmp.0[2] = u64::from_le_bytes(repr[16..24].try_into().unwrap());\n tmp.0[3] = u64::from_le_bytes(repr[24..32].try_into().unwrap());\n\n // Try to subtract the modulus\n let (_, borrow) = sbb(tmp.0[0], MODULUS.0[0], 0);\n let (_, borrow) = sbb(tmp.0[1], MODULUS.0[1], borrow);\n let (_, borrow) = sbb(tmp.0[2], MODULUS.0[2], borrow);\n let (_, borrow) = sbb(tmp.0[3], MODULUS.0[3], borrow);\n\n // If the element is smaller than MODULUS then the\n // subtraction will underflow, producing a borrow value\n // of 0xffff...ffff. Otherwise, it'll be zero.\n let is_some = (borrow as u8) & 1;\n\n // Convert to Montgomery form by computing\n // (a.R^0 * R^2) / R = a.R\n tmp *= &R2;\n\n CtOption::new(tmp, Choice::from(is_some))\n }\n\n fn to_repr(&self) -> Self::Repr {\n // Turn into canonical form by computing\n // (a.R) / R = a\n let tmp = Fp::montgomery_reduce(self.0[0], self.0[1], self.0[2], self.0[3], 0, 0, 0, 0);\n\n let mut res = [0; 32];\n res[0..8].copy_from_slice(&tmp.0[0].to_le_bytes());\n res[8..16].copy_from_slice(&tmp.0[1].to_le_bytes());\n res[16..24].copy_from_slice(&tmp.0[2].to_le_bytes());\n res[24..32].copy_from_slice(&tmp.0[3].to_le_bytes());\n\n res\n }\n\n fn is_odd(&self) -> Choice {\n Choice::from(self.to_repr()[0] & 1)\n }\n}\n\n#[cfg(all(feature = \"bits\", not(target_pointer_width = \"64\")))]\ntype ReprBits = [u32; 8];\n\n#[cfg(all(feature = \"bits\", target_pointer_width = \"64\"))]\ntype ReprBits = [u64; 4];\n\n#[cfg(feature = \"bits\")]\n#[cfg_attr(docsrs, doc(cfg(feature = \"bits\")))]\nimpl PrimeFieldBits for Fp {\n type ReprBits = ReprBits;\n\n fn to_le_bits(&self) -> FieldBits<Self::ReprBits> {\n let bytes = self.to_repr();\n\n #[cfg(not(target_pointer_width = \"64\"))]\n let limbs = [\n u32::from_le_bytes(bytes[0..4].try_into().unwrap()),\n u32::from_le_bytes(bytes[4..8].try_into().unwrap()),\n u32::from_le_bytes(bytes[8..12].try_into().unwrap()),\n u32::from_le_bytes(bytes[12..16].try_into().unwrap()),\n u32::from_le_bytes(bytes[16..20].try_into().unwrap()),\n u32::from_le_bytes(bytes[20..24].try_into().unwrap()),\n u32::from_le_bytes(bytes[24..28].try_into().unwrap()),\n u32::from_le_bytes(bytes[28..32].try_into().unwrap()),\n ];\n\n #[cfg(target_pointer_width = \"64\")]\n let limbs = [\n u64::from_le_bytes(bytes[0..8].try_into().unwrap()),\n u64::from_le_bytes(bytes[8..16].try_into().unwrap()),\n u64::from_le_bytes(bytes[16..24].try_into().unwrap()),\n u64::from_le_bytes(bytes[24..32].try_into().unwrap()),\n ];\n\n FieldBits::new(limbs)\n }\n\n fn char_le_bits() -> FieldBits<Self::ReprBits> {\n #[cfg(not(target_pointer_width = \"64\"))]\n {\n FieldBits::new(MODULUS_LIMBS_32)\n }\n\n #[cfg(target_pointer_width = \"64\")]\n FieldBits::new(MODULUS.0)\n }\n}\n\n#[cfg(feature = \"sqrt-table\")]\nlazy_static! {\n // The perfect hash parameters are found by `squareroottab.sage` in zcash/pasta.\n #[cfg_attr(docsrs, doc(cfg(feature = \"sqrt-table\")))]\n static ref FP_TABLES: SqrtTables<Fp> = SqrtTables::new(0x11BE, 1098);\n}\n\nimpl SqrtTableHelpers for Fp {\n fn pow_by_t_minus1_over2(&self) -> Self {\n let sqr = |x: Fp, i: u32| (0..i).fold(x, |x, _| x.square());\n\n let r10 = self.square();\n let r11 = r10 * self;\n let r110 = r11.square();\n let r111 = r110 * self;\n let r1001 = r111 * r10;\n let r1101 = r111 * r110;\n let ra = sqr(*self, 129) * self;\n let rb = sqr(ra, 7) * r1001;\n let rc = sqr(rb, 7) * r1101;\n let rd = sqr(rc, 4) * r11;\n let re = sqr(rd, 6) * r111;\n let rf = sqr(re, 3) * r111;\n let rg = sqr(rf, 10) * r1001;\n let rh = sqr(rg, 5) * r1001;\n let ri = sqr(rh, 4) * r1001;\n let rj = sqr(ri, 3) * r111;\n let rk = sqr(rj, 4) * r1001;\n let rl = sqr(rk, 5) * r11;\n let rm = sqr(rl, 4) * r111;\n let rn = sqr(rm, 4) * r11;\n let ro = sqr(rn, 6) * r1001;\n let rp = sqr(ro, 5) * r1101;\n let rq = sqr(rp, 4) * r11;\n let rr = sqr(rq, 7) * r111;\n let rs = sqr(rr, 3) * r11;\n rs.square() // rt\n }\n\n fn get_lower_32(&self) -> u32 {\n // TODO: don't reduce, just hash the Montgomery form. (Requires rebuilding perfect hash table.)\n let tmp = Fp::montgomery_reduce(self.0[0], self.0[1], self.0[2], self.0[3], 0, 0, 0, 0);\n\n tmp.0[0] as u32\n }\n}\n\nimpl WithSmallOrderMulGroup<3> for Fp {\n const ZETA: Self = Fp::from_raw([\n 0x1dad5ebdfdfe4ab9,\n 0x1d1f8bd237ad3149,\n 0x2caad5dc57aab1b0,\n 0x12ccca834acdba71,\n ]);\n}\n\nimpl FromUniformBytes<64> for Fp {\n /// Converts a 512-bit little endian integer into\n /// a `Fp` by reducing by the modulus.\n fn from_uniform_bytes(bytes: &[u8; 64]) -> Fp {\n Fp::from_u512([\n u64::from_le_bytes(bytes[0..8].try_into().unwrap()),\n u64::from_le_bytes(bytes[8..16].try_into().unwrap()),\n u64::from_le_bytes(bytes[16..24].try_into().unwrap()),\n u64::from_le_bytes(bytes[24..32].try_into().unwrap()),\n u64::from_le_bytes(bytes[32..40].try_into().unwrap()),\n u64::from_le_bytes(bytes[40..48].try_into().unwrap()),\n u64::from_le_bytes(bytes[48..56].try_into().unwrap()),\n u64::from_le_bytes(bytes[56..64].try_into().unwrap()),\n ])\n }\n}\n\n#[cfg(feature = \"gpu\")]\nimpl ec_gpu::GpuName for Fp {\n fn name() -> alloc::string::String {\n ec_gpu::name!()\n }\n}\n\n#[cfg(feature = \"gpu\")]\nimpl ec_gpu::GpuField for Fp {\n fn one() -> alloc::vec::Vec<u32> {\n crate::fields::u64_to_u32(&R.0[..])\n }\n\n fn r2() -> alloc::vec::Vec<u32> {\n crate::fields::u64_to_u32(&R2.0[..])\n }\n\n fn modulus() -> alloc::vec::Vec<u32> {\n crate::fields::u64_to_u32(&MODULUS.0[..])\n }\n}\n\n#[test]\nfn test_inv() {\n // Compute -(r^{-1} mod 2^64) mod 2^64 by exponentiating\n // by totient(2**64) - 1\n\n let mut inv = 1u64;\n for _ in 0..63 {\n inv = inv.wrapping_mul(inv);\n inv = inv.wrapping_mul(MODULUS.0[0]);\n }\n inv = inv.wrapping_neg();\n\n assert_eq!(inv, INV);\n}\n\n#[test]\nfn test_sqrt() {\n // NB: TWO_INV is standing in as a \"random\" field element\n let v = (Fp::TWO_INV).square().sqrt().unwrap();\n assert!(v == Fp::TWO_INV || (-v) == Fp::TWO_INV);\n}\n\n#[test]\nfn test_sqrt_32bit_overflow() {\n assert!((Fp::from(5)).sqrt().is_none().unwrap_u8() == 1);\n}\n\n#[test]\nfn test_pow_by_t_minus1_over2() {\n // NB: TWO_INV is standing in as a \"random\" field element\n let v = (Fp::TWO_INV).pow_by_t_minus1_over2();\n assert!(v == ff::Field::pow_vartime(&Fp::TWO_INV, &T_MINUS1_OVER2));\n}\n\n#[test]\nfn test_sqrt_ratio_and_alt() {\n // (true, sqrt(num/div)), if num and div are nonzero and num/div is a square in the field\n let num = (Fp::TWO_INV).square();\n let div = Fp::from(25);\n let div_inverse = div.invert().unwrap();\n let expected = Fp::TWO_INV * Fp::from(5).invert().unwrap();\n let (is_square, v) = Fp::sqrt_ratio(&num, &div);\n assert!(bool::from(is_square));\n assert!(v == expected || (-v) == expected);\n\n let (is_square_alt, v_alt) = Fp::sqrt_alt(&(num * div_inverse));\n assert!(bool::from(is_square_alt));\n assert!(v_alt == v);\n\n // (false, sqrt(ROOT_OF_UNITY * num/div)), if num and div are nonzero and num/div is a nonsquare in the field\n let num = num * Fp::ROOT_OF_UNITY;\n let expected = Fp::TWO_INV * Fp::ROOT_OF_UNITY * Fp::from(5).invert().unwrap();\n let (is_square, v) = Fp::sqrt_ratio(&num, &div);\n assert!(!bool::from(is_square));\n assert!(v == expected || (-v) == expected);\n\n let (is_square_alt, v_alt) = Fp::sqrt_alt(&(num * div_inverse));\n assert!(!bool::from(is_square_alt));\n assert!(v_alt == v);\n\n // (true, 0), if num is zero\n let num = Fp::zero();\n let expected = Fp::zero();\n let (is_square, v) = Fp::sqrt_ratio(&num, &div);\n assert!(bool::from(is_square));\n assert!(v == expected);\n\n let (is_square_alt, v_alt) = Fp::sqrt_alt(&(num * div_inverse));\n assert!(bool::from(is_square_alt));\n assert!(v_alt == v);\n\n // (false, 0), if num is nonzero and div is zero\n let num = (Fp::TWO_INV).square();\n let div = Fp::zero();\n let expected = Fp::zero();\n let (is_square, v) = Fp::sqrt_ratio(&num, &div);\n assert!(!bool::from(is_square));\n assert!(v == expected);\n}\n\n#[test]\nfn test_zeta() {\n assert_eq!(\n format!(\"{:?}\", Fp::ZETA),\n \"0x12ccca834acdba712caad5dc57aab1b01d1f8bd237ad31491dad5ebdfdfe4ab9\"\n );\n\n let a = Fp::ZETA;\n assert!(a != Fp::one());\n let b = a * a;\n assert!(b != Fp::one());\n let c = b * a;\n assert!(c == Fp::one());\n}\n\n#[test]\nfn test_root_of_unity() {\n assert_eq!(\n Fp::ROOT_OF_UNITY.pow_vartime(&[1 << Fp::S, 0, 0, 0]),\n Fp::one()\n );\n}\n\n#[test]\nfn test_inv_root_of_unity() {\n assert_eq!(Fp::ROOT_OF_UNITY_INV, Fp::ROOT_OF_UNITY.invert().unwrap());\n}\n\n#[test]\nfn test_inv_2() {\n assert_eq!(Fp::TWO_INV, Fp::from(2).invert().unwrap());\n}\n\n#[test]\nfn test_delta() {\n assert_eq!(Fp::DELTA, GENERATOR.pow(&[1u64 << Fp::S, 0, 0, 0]));\n assert_eq!(\n Fp::DELTA,\n Fp::MULTIPLICATIVE_GENERATOR.pow(&[1u64 << Fp::S, 0, 0, 0])\n );\n}\n\n#[cfg(not(target_pointer_width = \"64\"))]\n#[test]\nfn consistent_modulus_limbs() {\n for (a, &b) in MODULUS\n .0\n .iter()\n .flat_map(|&limb| {\n Some(limb as u32)\n .into_iter()\n .chain(Some((limb >> 32) as u32))\n })\n .zip(MODULUS_LIMBS_32.iter())\n {\n assert_eq!(a, b);\n }\n}\n\n#[test]\nfn test_from_u512() {\n assert_eq!(\n Fp::from_raw([\n 0x3daec14d565241d9,\n 0x0b7af45b6073944b,\n 0xea5b8bd611a5bd4c,\n 0x150160330625db3d\n ]),\n Fp::from_u512([\n 0xee155641297678a1,\n 0xd83e156bdbfdbe65,\n 0xd9ccd834c68ba0b5,\n 0xf508ede312272758,\n 0x038df7cbf8228e89,\n 0x3505a1e4a3c74b41,\n 0xbfa46f775eb82db3,\n 0x26ebe27e262f471d\n ])\n );\n}\n"},{"id":3,"name":{"Local":"src/macros.rs"},"crate_name":"pasta_curves","contents":"macro_rules! impl_add_binop_specify_output {\n ($lhs:ident, $rhs:ident, $output:ident) => {\n impl<'b> ::core::ops::Add<&'b $rhs> for $lhs {\n type Output = $output;\n\n #[inline]\n fn add(self, rhs: &'b $rhs) -> $output {\n &self + rhs\n }\n }\n\n impl<'a> ::core::ops::Add<$rhs> for &'a $lhs {\n type Output = $output;\n\n #[inline]\n fn add(self, rhs: $rhs) -> $output {\n self + &rhs\n }\n }\n\n impl ::core::ops::Add<$rhs> for $lhs {\n type Output = $output;\n\n #[inline]\n fn add(self, rhs: $rhs) -> $output {\n &self + &rhs\n }\n }\n };\n}\n\nmacro_rules! impl_sub_binop_specify_output {\n ($lhs:ident, $rhs:ident, $output:ident) => {\n impl<'b> ::core::ops::Sub<&'b $rhs> for $lhs {\n type Output = $output;\n\n #[inline]\n fn sub(self, rhs: &'b $rhs) -> $output {\n &self - rhs\n }\n }\n\n impl<'a> ::core::ops::Sub<$rhs> for &'a $lhs {\n type Output = $output;\n\n #[inline]\n fn sub(self, rhs: $rhs) -> $output {\n self - &rhs\n }\n }\n\n impl ::core::ops::Sub<$rhs> for $lhs {\n type Output = $output;\n\n #[inline]\n fn sub(self, rhs: $rhs) -> $output {\n &self - &rhs\n }\n }\n };\n}\n\nmacro_rules! impl_binops_additive_specify_output {\n ($lhs:ident, $rhs:ident, $output:ident) => {\n impl_add_binop_specify_output!($lhs, $rhs, $output);\n impl_sub_binop_specify_output!($lhs, $rhs, $output);\n };\n}\n\nmacro_rules! impl_binops_multiplicative_mixed {\n ($lhs:ident, $rhs:ident, $output:ident) => {\n impl<'b> ::core::ops::Mul<&'b $rhs> for $lhs {\n type Output = $output;\n\n #[inline]\n fn mul(self, rhs: &'b $rhs) -> $output {\n &self * rhs\n }\n }\n\n impl<'a> ::core::ops::Mul<$rhs> for &'a $lhs {\n type Output = $output;\n\n #[inline]\n fn mul(self, rhs: $rhs) -> $output {\n self * &rhs\n }\n }\n\n impl ::core::ops::Mul<$rhs> for $lhs {\n type Output = $output;\n\n #[inline]\n fn mul(self, rhs: $rhs) -> $output {\n &self * &rhs\n }\n }\n };\n}\n\nmacro_rules! impl_binops_additive {\n ($lhs:ident, $rhs:ident) => {\n impl_binops_additive_specify_output!($lhs, $rhs, $lhs);\n\n impl ::core::ops::SubAssign<$rhs> for $lhs {\n #[inline]\n fn sub_assign(&mut self, rhs: $rhs) {\n *self = &*self - &rhs;\n }\n }\n\n impl ::core::ops::AddAssign<$rhs> for $lhs {\n #[inline]\n fn add_assign(&mut self, rhs: $rhs) {\n *self = &*self + &rhs;\n }\n }\n\n impl<'b> ::core::ops::SubAssign<&'b $rhs> for $lhs {\n #[inline]\n fn sub_assign(&mut self, rhs: &'b $rhs) {\n *self = &*self - rhs;\n }\n }\n\n impl<'b> ::core::ops::AddAssign<&'b $rhs> for $lhs {\n #[inline]\n fn add_assign(&mut self, rhs: &'b $rhs) {\n *self = &*self + rhs;\n }\n }\n };\n}\n\nmacro_rules! impl_binops_multiplicative {\n ($lhs:ident, $rhs:ident) => {\n impl_binops_multiplicative_mixed!($lhs, $rhs, $lhs);\n\n impl ::core::ops::MulAssign<$rhs> for $lhs {\n #[inline]\n fn mul_assign(&mut self, rhs: $rhs) {\n *self = &*self * &rhs;\n }\n }\n\n impl<'b> ::core::ops::MulAssign<&'b $rhs> for $lhs {\n #[inline]\n fn mul_assign(&mut self, rhs: &'b $rhs) {\n *self = &*self * rhs;\n }\n }\n };\n}\n"},{"id":4,"name":{"Local":"/rustc/library/core/src/clone.rs"},"crate_name":"core","contents":null},{"id":5,"name":{"Local":"/rustc/library/core/src/lib.rs"},"crate_name":"core","contents":null},{"id":6,"name":{"Local":"/rustc/library/core/src/marker.rs"},"crate_name":"core","contents":null},{"id":7,"name":{"Local":"/rustc/library/core/src/cmp.rs"},"crate_name":"core","contents":null},{"id":8,"name":{"Local":"/rustc/library/core/src/fmt/mod.rs"},"crate_name":"core","contents":null},{"id":9,"name":{"Local":"/rustc/library/core/src/convert/mod.rs"},"crate_name":"core","contents":null},{"id":10,"name":{"Local":"/cargo/registry/src/index.crates.io-1949cf8c6b5b557f/subtle-2.6.1/src/lib.rs"},"crate_name":"subtle","contents":null},{"id":11,"name":{"Local":"/rustc/library/core/src/option.rs"},"crate_name":"core","contents":null},{"id":12,"name":{"Local":"/rustc/library/core/src/ops/control_flow.rs"},"crate_name":"core","contents":null},{"id":13,"name":{"Local":"/rustc/library/core/src/ops/mod.rs"},"crate_name":"core","contents":null},{"id":14,"name":{"Local":"/rustc/library/core/src/ops/arith.rs"},"crate_name":"core","contents":null},{"id":15,"name":{"Local":"/rustc/library/core/src/borrow.rs"},"crate_name":"core","contents":null},{"id":16,"name":{"Local":"/rustc/library/core/src/iter/traits/accum.rs"},"crate_name":"core","contents":null},{"id":17,"name":{"Local":"/rustc/library/core/src/iter/traits/mod.rs"},"crate_name":"core","contents":null},{"id":18,"name":{"Local":"/rustc/library/core/src/iter/mod.rs"},"crate_name":"core","contents":null},{"id":19,"name":{"Local":"/rustc/library/core/src/iter/traits/iterator.rs"},"crate_name":"core","contents":null},{"id":20,"name":{"Local":"/rustc/library/core/src/default.rs"},"crate_name":"core","contents":null},{"id":21,"name":{"Local":"/cargo/registry/src/index.crates.io-1949cf8c6b5b557f/ff-0.13.1/src/lib.rs"},"crate_name":"ff","contents":null},{"id":22,"name":{"Local":"/cargo/registry/src/index.crates.io-1949cf8c6b5b557f/rand_core-0.6.4/src/lib.rs"},"crate_name":"rand_core","contents":null},{"id":23,"name":{"Local":"/rustc/library/core/src/array/mod.rs"},"crate_name":"core","contents":null},{"id":24,"name":{"Local":"src/arithmetic/fields.rs"},"crate_name":"pasta_curves","contents":"//! This module contains the `Field` abstraction that allows us to write\n//! code that generalizes over a pair of fields.\n\nuse core::mem::size_of;\n\nuse static_assertions::const_assert;\n\n#[cfg(feature = \"sqrt-table\")]\nuse alloc::{boxed::Box, vec::Vec};\n#[cfg(feature = \"sqrt-table\")]\nuse core::marker::PhantomData;\n\n#[cfg(feature = \"sqrt-table\")]\nuse subtle::Choice;\n\nconst_assert!(size_of::<usize>() >= 4);\n\n/// An internal trait that exposes additional operations related to calculating square roots of\n/// prime-order finite fields.\npub(crate) trait SqrtTableHelpers: ff::PrimeField {\n /// Raise this field element to the power $(t-1)/2$.\n ///\n /// Field implementations may override this to use an efficient addition chain.\n fn pow_by_t_minus1_over2(&self) -> Self;\n\n /// Gets the lower 32 bits of this field element when expressed\n /// canonically.\n fn get_lower_32(&self) -> u32;\n}\n\n/// Parameters for a perfect hash function used in square root computation.\n#[cfg(feature = \"sqrt-table\")]\n#[cfg_attr(docsrs, doc(cfg(feature = \"sqrt-table\")))]\n#[derive(Debug)]\nstruct SqrtHasher<F: SqrtTableHelpers> {\n hash_xor: u32,\n hash_mod: usize,\n marker: PhantomData<F>,\n}\n\n#[cfg(feature = \"sqrt-table\")]\nimpl<F: SqrtTableHelpers> SqrtHasher<F> {\n /// Returns a perfect hash of x for use with SqrtTables::inv.\n fn hash(&self, x: &F) -> usize {\n // This is just the simplest constant-time perfect hash construction that could\n // possibly work. The 32 low-order bits are unique within the 2^S order subgroup,\n // then the xor acts as \"salt\" to injectively randomize the output when taken modulo\n // `hash_mod`. Since the table is small, we do not need anything more complicated.\n ((x.get_lower_32() ^ self.hash_xor) as usize) % self.hash_mod\n }\n}\n\n/// Tables used for square root computation.\n#[cfg(feature = \"sqrt-table\")]\n#[cfg_attr(docsrs, doc(cfg(feature = \"sqrt-table\")))]\n#[derive(Debug)]\npub(crate) struct SqrtTables<F: SqrtTableHelpers> {\n hasher: SqrtHasher<F>,\n inv: Vec<u8>,\n g0: Box<[F; 256]>,\n g1: Box<[F; 256]>,\n g2: Box<[F; 256]>,\n g3: Box<[F; 129]>,\n}\n\n#[cfg(feature = \"sqrt-table\")]\nimpl<F: SqrtTableHelpers> SqrtTables<F> {\n /// Build tables given parameters for the perfect hash.\n pub fn new(hash_xor: u32, hash_mod: usize) -> Self {\n use alloc::vec;\n\n let hasher = SqrtHasher {\n hash_xor,\n hash_mod,\n marker: PhantomData,\n };\n\n let mut gtab = (0..4).scan(F::ROOT_OF_UNITY, |gi, _| {\n // gi == ROOT_OF_UNITY^(256^i)\n let gtab_i: Vec<F> = (0..256)\n .scan(F::ONE, |acc, _| {\n let res = *acc;\n *acc *= *gi;\n Some(res)\n })\n .collect();\n *gi = gtab_i[255] * *gi;\n Some(gtab_i)\n });\n let gtab_0 = gtab.next().unwrap();\n let gtab_1 = gtab.next().unwrap();\n let gtab_2 = gtab.next().unwrap();\n let mut gtab_3 = gtab.next().unwrap();\n assert_eq!(gtab.next(), None);\n\n // Now invert gtab[3].\n let mut inv: Vec<u8> = vec![1; hash_mod];\n for (j, gtab_3_j) in gtab_3.iter().enumerate() {\n let hash = hasher.hash(gtab_3_j);\n // 1 is the last value to be assigned, so this ensures there are no collisions.\n assert!(inv[hash] == 1);\n inv[hash] = ((256 - j) & 0xFF) as u8;\n }\n\n gtab_3.truncate(129);\n\n SqrtTables::<F> {\n hasher,\n inv,\n g0: gtab_0.into_boxed_slice().try_into().unwrap(),\n g1: gtab_1.into_boxed_slice().try_into().unwrap(),\n g2: gtab_2.into_boxed_slice().try_into().unwrap(),\n g3: gtab_3.into_boxed_slice().try_into().unwrap(),\n }\n }\n\n /// Computes:\n ///\n /// * (true, sqrt(num/div)), if num and div are nonzero and num/div is a square in the field;\n /// * (true, 0), if num is zero;\n /// * (false, 0), if num is nonzero and div is zero;\n /// * (false, sqrt(ROOT_OF_UNITY * num/div)), if num and div are nonzero and num/div is a nonsquare in the field;\n ///\n /// where ROOT_OF_UNITY is a generator of the order 2^n subgroup (and therefore a nonsquare).\n ///\n /// The choice of root from sqrt is unspecified.\n pub fn sqrt_ratio(&self, num: &F, div: &F) -> (Choice, F) {\n // Based on:\n // * [Sarkar2020](https://eprint.iacr.org/2020/1407)\n // * [BDLSY2012](https://cr.yp.to/papers.html#ed25519)\n //\n // We need to calculate uv and v, where v = u^((T-1)/2), u = num/div, and p-1 = T * 2^S.\n // We can rewrite as follows:\n //\n // v = (num/div)^((T-1)/2)\n // = num^((T-1)/2) * div^(p-1 - (T-1)/2) [Fermat's Little Theorem]\n // = \" * div^(T * 2^S - (T-1)/2)\n // = \" * div^((2^(S+1) - 1)*(T-1)/2 + 2^S)\n // = (num * div^(2^(S+1) - 1))^((T-1)/2) * div^(2^S)\n //\n // Let w = (num * div^(2^(S+1) - 1))^((T-1)/2) * div^(2^S - 1).\n // Then v = w * div, and uv = num * v / div = num * w.\n //\n // We calculate:\n //\n // s = div^(2^S - 1) using an addition chain\n // t = div^(2^(S+1) - 1) = s^2 * div\n // w = (num * t)^((T-1)/2) * s using another addition chain\n //\n // then u and uv as above. The addition chains are given in\n // https://github.com/zcash/pasta/blob/master/addchain_sqrt.py .\n // The overall cost of this part is similar to a single full-width exponentiation,\n // regardless of S.\n\n let sqr = |x: F, i: u32| (0..i).fold(x, |x, _| x.square());\n\n // s = div^(2^S - 1)\n let s = (0..5).fold(*div, |d: F, i| sqr(d, 1 << i) * d);\n\n // t == div^(2^(S+1) - 1)\n let t = s.square() * div;\n\n // w = (num * t)^((T-1)/2) * s\n let w = (t * num).pow_by_t_minus1_over2() * s;\n\n // v == u^((T-1)/2)\n let v = w * div;\n\n // uv = u * v\n let uv = w * num;\n\n let res = self.sqrt_common(&uv, &v);\n\n let sqdiv = res.square() * div;\n let is_square = (sqdiv - num).is_zero();\n let is_nonsquare = (sqdiv - F::ROOT_OF_UNITY * num).is_zero();\n assert!(bool::from(\n num.is_zero() | div.is_zero() | (is_square ^ is_nonsquare)\n ));\n\n (is_square, res)\n }\n\n /// Same as sqrt_ratio(u, one()) but more efficient.\n pub fn sqrt_alt(&self, u: &F) -> (Choice, F) {\n let v = u.pow_by_t_minus1_over2();\n let uv = *u * v;\n\n let res = self.sqrt_common(&uv, &v);\n\n let sq = res.square();\n let is_square = (sq - u).is_zero();\n let is_nonsquare = (sq - F::ROOT_OF_UNITY * u).is_zero();\n assert!(bool::from(u.is_zero() | (is_square ^ is_nonsquare)));\n\n (is_square, res)\n }\n\n /// Common part of sqrt_ratio and sqrt_alt: return their result given v = u^((T-1)/2) and uv = u * v.\n fn sqrt_common(&self, uv: &F, v: &F) -> F {\n let sqr = |x: F, i: u32| (0..i).fold(x, |x, _| x.square());\n let inv = |x: F| self.inv[self.hasher.hash(&x)] as usize;\n\n let x3 = *uv * v;\n let x2 = sqr(x3, 8);\n let x1 = sqr(x2, 8);\n let x0 = sqr(x1, 8);\n\n // i = 0, 1\n let mut t_ = inv(x0); // = t >> 16\n // 1 == x0 * ROOT_OF_UNITY^(t_ << 24)\n assert!(t_ < 0x100);\n let alpha = x1 * self.g2[t_];\n\n // i = 2\n t_ += inv(alpha) << 8; // = t >> 8\n // 1 == x1 * ROOT_OF_UNITY^(t_ << 16)\n assert!(t_ < 0x10000);\n let alpha = x2 * self.g1[t_ & 0xFF] * self.g2[t_ >> 8];\n\n // i = 3\n t_ += inv(alpha) << 16; // = t\n // 1 == x2 * ROOT_OF_UNITY^(t_ << 8)\n assert!(t_ < 0x1000000);\n let alpha = x3 * self.g0[t_ & 0xFF] * self.g1[(t_ >> 8) & 0xFF] * self.g2[t_ >> 16];\n\n t_ += inv(alpha) << 24; // = t << 1\n // 1 == x3 * ROOT_OF_UNITY^t_\n t_ = (((t_ as u64) + 1) >> 1) as usize;\n assert!(t_ <= 0x80000000);\n\n *uv * self.g0[t_ & 0xFF]\n * self.g1[(t_ >> 8) & 0xFF]\n * self.g2[(t_ >> 16) & 0xFF]\n * self.g3[t_ >> 24]\n }\n}\n\n/// Compute a + b + carry, returning the result and the new carry over.\n#[inline(always)]\npub(crate) const fn adc(a: u64, b: u64, carry: u64) -> (u64, u64) {\n let ret = (a as u128) + (b as u128) + (carry as u128);\n (ret as u64, (ret >> 64) as u64)\n}\n\n/// Compute a - (b + borrow), returning the result and the new borrow.\n#[inline(always)]\npub(crate) const fn sbb(a: u64, b: u64, borrow: u64) -> (u64, u64) {\n let ret = (a as u128).wrapping_sub((b as u128) + ((borrow >> 63) as u128));\n (ret as u64, (ret >> 64) as u64)\n}\n\n/// Compute a + (b * c) + carry, returning the result and the new carry over.\n#[inline(always)]\npub(crate) const fn mac(a: u64, b: u64, c: u64, carry: u64) -> (u64, u64) {\n let ret = (a as u128) + ((b as u128) * (c as u128)) + (carry as u128);\n (ret as u64, (ret >> 64) as u64)\n}\n"},{"id":25,"name":{"Local":"src/arithmetic.rs"},"crate_name":"pasta_curves","contents":"//! This module provides common utilities, traits and structures for group and\n//! field arithmetic.\n//!\n//! This module is temporary, and the extension traits defined here are expected to be\n//! upstreamed into the `ff` and `group` crates after some refactoring.\n\nmod curves;\nmod fields;\n\npub use curves::*;\npub(crate) use 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Examples"},{"DocComment":""},{"DocComment":" Early-exiting from [`Iterator::try_for_each`]:"},{"DocComment":" ```"},{"DocComment":" use std::ops::ControlFlow;"},{"DocComment":""},{"DocComment":" let r = (2..100).try_for_each(|x| {"},{"DocComment":" if 403 % x == 0 {"},{"DocComment":" return ControlFlow::Break(x)"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" ControlFlow::Continue(())"},{"DocComment":" });"},{"DocComment":" assert_eq!(r, ControlFlow::Break(13));"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" A basic tree traversal:"},{"DocComment":" ```"},{"DocComment":" use std::ops::ControlFlow;"},{"DocComment":""},{"DocComment":" pub struct TreeNode<T> {"},{"DocComment":" value: T,"},{"DocComment":" left: Option<Box<TreeNode<T>>>,"},{"DocComment":" right: Option<Box<TreeNode<T>>>,"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl<T> TreeNode<T> {"},{"DocComment":" pub fn traverse_inorder<B>(&self, f: &mut impl FnMut(&T) -> ControlFlow<B>) -> ControlFlow<B> {"},{"DocComment":" if let Some(left) = &self.left {"},{"DocComment":" left.traverse_inorder(f)?;"},{"DocComment":" }"},{"DocComment":" f(&self.value)?;"},{"DocComment":" if let Some(right) = &self.right {"},{"DocComment":" right.traverse_inorder(f)?;"},{"DocComment":" }"},{"DocComment":" ControlFlow::Continue(())"},{"DocComment":" }"},{"DocComment":" fn leaf(value: T) -> Option<Box<TreeNode<T>>> {"},{"DocComment":" Some(Box::new(Self { value, left: None, right: None }))"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" let node = TreeNode {"},{"DocComment":" value: 0,"},{"DocComment":" left: TreeNode::leaf(1),"},{"DocComment":" right: Some(Box::new(TreeNode {"},{"DocComment":" value: -1,"},{"DocComment":" left: TreeNode::leaf(5),"},{"DocComment":" right: TreeNode::leaf(2),"},{"DocComment":" }))"},{"DocComment":" };"},{"DocComment":" let mut sum = 0;"},{"DocComment":""},{"DocComment":" let res = node.traverse_inorder(&mut |val| {"},{"DocComment":" if *val < 0 {"},{"DocComment":" ControlFlow::Break(*val)"},{"DocComment":" } else {"},{"DocComment":" sum += *val;"},{"DocComment":" ControlFlow::Continue(())"},{"DocComment":" }"},{"DocComment":" });"},{"DocComment":" assert_eq!(res, ControlFlow::Break(-1));"},{"DocComment":" assert_eq!(sum, 6);"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" [`Break`]: ControlFlow::Break"},{"DocComment":" [`Continue`]: ControlFlow::Continue"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"ControlFlow"},"generics":{"regions":[],"types":[{"index":0,"name":"B"},{"index":1,"name":"C"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"src":"TopLevel","kind":{"Enum":[{"id":0,"span":{"data":{"file_id":12,"beg":{"line":93,"col":4},"end":{"line":93,"col":12}},"generated_from_span":null},"attr_info":{"attributes":[{"DocComment":" Move on to the next phase of the operation as normal."}],"inline":null,"rename":null,"public":true},"name":"Continue","fields":[{"span":{"data":{"file_id":12,"beg":{"line":93,"col":13},"end":{"line":93,"col":14}},"generated_from_span":null},"attr_info":{"attributes":[],"inline":null,"rename":null,"public":true},"name":null,"ty":{"HashConsedValue":[8295,{"TypeVar":{"Free":1}}]}}],"discriminant":{"Scalar":{"Signed":["Isize","0"]}}},{"id":1,"span":{"data":{"file_id":12,"beg":{"line":97,"col":4},"end":{"line":97,"col":9}},"generated_from_span":null},"attr_info":{"attributes":[{"DocComment":" Exit the operation without running subsequent phases."}],"inline":null,"rename":null,"public":true},"name":"Break","fields":[{"span":{"data":{"file_id":12,"beg":{"line":97,"col":10},"end":{"line":97,"col":11}},"generated_from_span":null},"attr_info":{"attributes":[],"inline":null,"rename":null,"public":true},"name":null,"ty":{"Deduplicated":8294}}],"discriminant":{"Scalar":{"Signed":["Isize","1"]}}}]},"layout":[],"ptr_metadata":"None"},{"def_id":7,"item_meta":{"name":[{"Ident":["subtle",0]},{"Ident":["CtOption",0]}],"span":{"data":{"file_id":10,"beg":{"line":647,"col":0},"end":{"line":647,"col":22}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" The `CtOption<T>` type represents an optional value similar to the"},{"DocComment":" [`Option<T>`](core::option::Option) type but is intended for"},{"DocComment":" use in constant time APIs."},{"DocComment":""},{"DocComment":" Any given `CtOption<T>` is either `Some` or `None`, but unlike"},{"DocComment":" `Option<T>` these variants are not exposed. The"},{"DocComment":" [`is_some()`](CtOption::is_some) method is used to determine if"},{"DocComment":" the value is `Some`, and [`unwrap_or()`](CtOption::unwrap_or) and"},{"DocComment":" [`unwrap_or_else()`](CtOption::unwrap_or_else) methods are"},{"DocComment":" provided to access the underlying value. The value can also be"},{"DocComment":" obtained with [`unwrap()`](CtOption::unwrap) but this will panic"},{"DocComment":" if it is `None`."},{"DocComment":""},{"DocComment":" Functions that are intended to be constant time may not produce"},{"DocComment":" valid results for all inputs, such as square root and inversion"},{"DocComment":" operations in finite field arithmetic. Returning an `Option<T>`"},{"DocComment":" from these functions makes it difficult for the caller to reason"},{"DocComment":" about the result in constant time, and returning an incorrect"},{"DocComment":" value burdens the caller and increases the chance of bugs."}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":null},"generics":{"regions":[],"types":[{"index":0,"name":"T"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"src":"TopLevel","kind":"Opaque","layout":[],"ptr_metadata":"None"},null,{"def_id":9,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["fmt",0]},{"Ident":["Formatter",0]}],"span":{"data":{"file_id":8,"beg":{"line":561,"col":0},"end":{"line":561,"col":24}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" Configuration for formatting."},{"DocComment":""},{"DocComment":" A `Formatter` represents various options related to formatting. Users do not"},{"DocComment":" construct `Formatter`s directly; a mutable reference to one is passed to"},{"DocComment":" the `fmt` method of all formatting traits, like [`Debug`] and [`Display`]."},{"DocComment":""},{"DocComment":" To interact with a `Formatter`, you'll call various methods to change the"},{"DocComment":" various options related to formatting. For examples, please see the"},{"DocComment":" documentation of the methods defined on `Formatter` below."}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"Formatter"},"generics":{"regions":[{"index":0,"name":"'a","mutability":"Mutable"}],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[{"regions":[],"skip_binder":[{"Var":{"Free":0}},{"Var":{"Free":0}}]}],"types_outlive":[],"trait_type_constraints":[]},"src":"TopLevel","kind":"Opaque","layout":[{"key":"x86_64-unknown-linux-gnu","value":{"size":24,"align":8,"discriminator":{"Known":0},"uninhabited":false,"variant_layouts":[{"field_offsets":[16,0],"uninhabited":false,"tagger":[]}],"repr":{"repr_algo":"Rust","align_modif":null,"transparent":false,"explicit_discr_type":false}}}],"ptr_metadata":"None"},{"def_id":10,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["result",0]},{"Ident":["Result",0]}],"span":{"data":{"file_id":26,"beg":{"line":557,"col":0},"end":{"line":557,"col":21}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" `Result` is a type that represents either success ([`Ok`]) or failure ([`Err`])."},{"DocComment":""},{"DocComment":" See the [module documentation](self) for details."}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"Result"},"generics":{"regions":[],"types":[{"index":0,"name":"T"},{"index":1,"name":"E"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"src":"TopLevel","kind":{"Enum":[{"id":0,"span":{"data":{"file_id":26,"beg":{"line":561,"col":4},"end":{"line":561,"col":6}},"generated_from_span":null},"attr_info":{"attributes":[{"DocComment":" Contains the success value"}],"inline":null,"rename":null,"public":true},"name":"Ok","fields":[{"span":{"data":{"file_id":26,"beg":{"line":561,"col":53},"end":{"line":561,"col":54}},"generated_from_span":null},"attr_info":{"attributes":[],"inline":null,"rename":null,"public":true},"name":null,"ty":{"Deduplicated":8294}}],"discriminant":{"Scalar":{"Signed":["Isize","0"]}}},{"id":1,"span":{"data":{"file_id":26,"beg":{"line":566,"col":4},"end":{"line":566,"col":7}},"generated_from_span":null},"attr_info":{"attributes":[{"DocComment":" Contains the error value"}],"inline":null,"rename":null,"public":true},"name":"Err","fields":[{"span":{"data":{"file_id":26,"beg":{"line":566,"col":54},"end":{"line":566,"col":55}},"generated_from_span":null},"attr_info":{"attributes":[],"inline":null,"rename":null,"public":true},"name":null,"ty":{"Deduplicated":8295}}],"discriminant":{"Scalar":{"Signed":["Isize","1"]}}}]},"layout":[],"ptr_metadata":"None"},{"def_id":11,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["fmt",0]},{"Ident":["Error",0]}],"span":{"data":{"file_id":8,"beg":{"line":109,"col":0},"end":{"line":109,"col":16}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" The error type which is returned from formatting a message into a stream."},{"DocComment":""},{"DocComment":" This type does not support transmission of an error other than that an error"},{"DocComment":" occurred. This is because, despite the existence of this error,"},{"DocComment":" string formatting is considered an infallible operation."},{"DocComment":" `fmt()` implementors should not return this `Error` unless they received it from their"},{"DocComment":" [`Formatter`]. The only time your code should create a new instance of this"},{"DocComment":" error is when implementing `fmt::Write`, in order to cancel the formatting operation when"},{"DocComment":" writing to the underlying stream fails."},{"DocComment":""},{"DocComment":" Any extra information must be arranged to be transmitted through some other means,"},{"DocComment":" such as storing it in a field to be consulted after the formatting operation has been"},{"DocComment":" cancelled. (For example, this is how [`std::io::Write::write_fmt()`] propagates IO errors"},{"DocComment":" during writing.)"},{"DocComment":""},{"DocComment":" This type, `fmt::Error`, should not be"},{"DocComment":" confused with [`std::io::Error`] or [`std::error::Error`], which you may also"},{"DocComment":" have in scope."},{"DocComment":""},{"DocComment":" [`std::io::Error`]: ../../std/io/struct.Error.html"},{"DocComment":" [`std::io::Write::write_fmt()`]: ../../std/io/trait.Write.html#method.write_fmt"},{"DocComment":" [`std::error::Error`]: ../../std/error/trait.Error.html"},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" ```rust"},{"DocComment":" use std::fmt::{self, write};"},{"DocComment":""},{"DocComment":" let mut output = String::new();"},{"DocComment":" if let Err(fmt::Error) = write(&mut output, format_args!(\"Hello {}!\", \"world\")) {"},{"DocComment":" panic!(\"An error occurred\");"},{"DocComment":" }"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":null},"generics":{"regions":[],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"src":"TopLevel","kind":{"Struct":[]},"layout":[{"key":"x86_64-unknown-linux-gnu","value":{"size":0,"align":1,"discriminator":{"Known":0},"uninhabited":false,"variant_layouts":[{"field_offsets":[],"uninhabited":false,"tagger":[]}],"repr":{"repr_algo":"Rust","align_modif":null,"transparent":false,"explicit_discr_type":false}}}],"ptr_metadata":"None"},null,null,null,null,null,null,null,null,null,{"def_id":21,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["array",0]},{"Ident":["iter",0]},{"Ident":["IntoIter",0]}],"span":{"data":{"file_id":27,"beg":{"line":20,"col":0},"end":{"line":20,"col":38}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" A by-value [array] iterator."}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"ArrayIntoIter"},"generics":{"regions":[],"types":[{"index":0,"name":"T"}],"const_generics":[{"index":0,"name":"N","ty":{"Deduplicated":1073}}],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"src":"TopLevel","kind":"Opaque","layout":[],"ptr_metadata":"None"},{"def_id":22,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["num",0]},{"Ident":["nonzero",0]},{"Ident":["NonZero",0]}],"span":{"data":{"file_id":28,"beg":{"line":128,"col":0},"end":{"line":128,"col":40}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" A value that is known not to equal zero."},{"DocComment":""},{"DocComment":" This enables some memory layout optimization."},{"DocComment":" For example, `Option<NonZero<u32>>` is the same size as `u32`:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" use core::{num::NonZero};"},{"DocComment":""},{"DocComment":" assert_eq!(size_of::<Option<NonZero<u32>>>(), size_of::<u32>());"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" # Layout"},{"DocComment":""},{"DocComment":" `NonZero<T>` is guaranteed to have the same layout and bit validity as `T`"},{"DocComment":" with the exception that the all-zero bit pattern is invalid."},{"DocComment":" `Option<NonZero<T>>` is guaranteed to be compatible with `T`, including in"},{"DocComment":" FFI."},{"DocComment":""},{"DocComment":" Thanks to the [null pointer optimization], `NonZero<T>` and"},{"DocComment":" `Option<NonZero<T>>` are guaranteed to have the same size and alignment:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" use std::num::NonZero;"},{"DocComment":""},{"DocComment":" assert_eq!(size_of::<NonZero<u32>>(), size_of::<Option<NonZero<u32>>>());"},{"DocComment":" assert_eq!(align_of::<NonZero<u32>>(), align_of::<Option<NonZero<u32>>>());"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" [null pointer optimization]: crate::option#representation"},{"DocComment":""},{"DocComment":" # Note on generic usage"},{"DocComment":""},{"DocComment":" `NonZero<T>` can only be used with some standard library primitive types"},{"DocComment":" (such as `u8`, `i32`, and etc.). The type parameter `T` must implement the"},{"DocComment":" internal trait [`ZeroablePrimitive`], which is currently permanently unstable"},{"DocComment":" and cannot be implemented by users. Therefore, you cannot use `NonZero<T>`"},{"DocComment":" with your own types, nor can you implement traits for all `NonZero<T>`,"},{"DocComment":" only for concrete types."}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"NonZero"},"generics":{"regions":[],"types":[{"index":0,"name":"T"},{"index":1,"name":"Clause0_NonZeroInner"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"src":"TopLevel","kind":"Opaque","layout":[],"ptr_metadata":"None"},{"def_id":23,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["iter",0]},{"Ident":["adapters",0]},{"Ident":["step_by",0]},{"Ident":["StepBy",0]}],"span":{"data":{"file_id":30,"beg":{"line":16,"col":0},"end":{"line":16,"col":20}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" An iterator for stepping iterators by a custom amount."},{"DocComment":""},{"DocComment":" This `struct` is created by the [`step_by`] method on [`Iterator`]. See"},{"DocComment":" its documentation for more."},{"DocComment":""},{"DocComment":" [`step_by`]: Iterator::step_by"},{"DocComment":" [`Iterator`]: trait.Iterator.html"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":null},"generics":{"regions":[],"types":[{"index":0,"name":"I"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"src":"TopLevel","kind":"Opaque","layout":[],"ptr_metadata":"None"},{"def_id":24,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["iter",0]},{"Ident":["adapters",0]},{"Ident":["chain",0]},{"Ident":["Chain",0]}],"span":{"data":{"file_id":33,"beg":{"line":23,"col":0},"end":{"line":23,"col":22}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" An iterator that links two iterators together, in a chain."},{"DocComment":""},{"DocComment":" This `struct` is created by [`chain`] or [`Iterator::chain`]. See their"},{"DocComment":" documentation for more."},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" use std::iter::Chain;"},{"DocComment":" use std::slice::Iter;"},{"DocComment":""},{"DocComment":" let a1 = [1, 2, 3];"},{"DocComment":" let a2 = [4, 5, 6];"},{"DocComment":" let iter: Chain<Iter<'_, _>, Iter<'_, _>> = a1.iter().chain(a2.iter());"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":null},"generics":{"regions":[],"types":[{"index":0,"name":"A"},{"index":1,"name":"B"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"src":"TopLevel","kind":"Opaque","layout":[],"ptr_metadata":"None"},{"def_id":25,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["iter",0]},{"Ident":["adapters",0]},{"Ident":["zip",0]},{"Ident":["Zip",0]}],"span":{"data":{"file_id":34,"beg":{"line":13,"col":0},"end":{"line":13,"col":20}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" An iterator that iterates two other iterators simultaneously."},{"DocComment":""},{"DocComment":" This `struct` is created by [`zip`] or [`Iterator::zip`]."},{"DocComment":" See their documentation for more."}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":null},"generics":{"regions":[],"types":[{"index":0,"name":"A"},{"index":1,"name":"B"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"src":"TopLevel","kind":"Opaque","layout":[],"ptr_metadata":"None"},{"def_id":26,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["iter",0]},{"Ident":["adapters",0]},{"Ident":["intersperse",0]},{"Ident":["Intersperse",0]}],"span":{"data":{"file_id":35,"beg":{"line":9,"col":0},"end":{"line":9,"col":35}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" An iterator adapter that places a separator between all elements."},{"DocComment":""},{"DocComment":" This `struct` is created by [`Iterator::intersperse`]. 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Returns a field element that is congruent to the provided little endian unsigned"},{"DocComment":" byte representation of an integer."}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":null},"generics":{"regions":[{"index":0,"name":null,"mutability":"Unknown"}],"types":[{"index":0,"name":"Self"},{"index":1,"name":"Clause0_Clause0_Repr"}],"const_generics":[{"index":0,"name":"N","ty":{"Deduplicated":1073}}],"trait_clauses":[{"clause_id":0,"span":{"data":{"file_id":1,"beg":{"line":1,"col":0},"end":{"line":1,"col":0}},"generated_from_span":null},"origin":"WhereClauseOnFn","trait_":{"regions":[],"skip_binder":{"id":33,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[{"kind":{"Var":{"Free":0}},"ty":{"Deduplicated":1073}}],"trait_refs":[]}}}}],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"HashConsedValue":[8467,{"Ref":[{"Var":{"Free":0}},{"HashConsedValue":[8398,{"Array":[{"Deduplicated":1894},{"kind":{"Var":{"Free":0}},"ty":{"Deduplicated":1073}}]}]},"Shared"]}]}],"output":{"Deduplicated":8294}},"src":{"TraitDecl":{"trait_ref":{"id":33,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[{"kind":{"Var":{"Free":0}},"ty":{"Deduplicated":1073}}],"trait_refs":[]}},"item_id":{"Method":0},"has_default":false}},"is_global_initializer":null,"body":"Opaque"},null,null,{"def_id":255,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["iter",0]},{"Ident":["traits",0]},{"Ident":["collect",0]},{"Ident":["IntoIterator",0]},{"Ident":["into_iter",0]}],"span":{"data":{"file_id":32,"beg":{"line":312,"col":4},"end":{"line":312,"col":41}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" Creates an iterator from a value."},{"DocComment":""},{"DocComment":" See the [module-level documentation] for more."},{"DocComment":""},{"DocComment":" [module-level documentation]: crate::iter"},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" let v = [1, 2, 3];"},{"DocComment":" let mut iter = v.into_iter();"},{"DocComment":""},{"DocComment":" assert_eq!(Some(1), iter.next());"},{"DocComment":" assert_eq!(Some(2), iter.next());"},{"DocComment":" assert_eq!(Some(3), iter.next());"},{"DocComment":" assert_eq!(None, iter.next());"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"into_iter"},"generics":{"regions":[],"types":[{"index":0,"name":"Self"},{"index":1,"name":"Clause0_Item"},{"index":2,"name":"Clause0_IntoIter"}],"const_generics":[],"trait_clauses":[{"clause_id":0,"span":{"data":{"file_id":1,"beg":{"line":1,"col":0},"end":{"line":1,"col":0}},"generated_from_span":null},"origin":"WhereClauseOnFn","trait_":{"regions":[],"skip_binder":{"id":35,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295},{"Deduplicated":8348}],"const_generics":[],"trait_refs":[]}}}}],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8294}],"output":{"Deduplicated":8348}},"src":{"TraitDecl":{"trait_ref":{"id":35,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295},{"Deduplicated":8348}],"const_generics":[],"trait_refs":[]}},"item_id":{"Method":0},"has_default":false}},"is_global_initializer":null,"body":"Opaque"},{"def_id":256,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["ops",0]},{"Ident":["function",0]},{"Ident":["FnMut",0]},{"Ident":["call_mut",0]}],"span":{"data":{"file_id":36,"beg":{"line":166,"col":4},"end":{"line":166,"col":74}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" Performs the call 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Performs the call 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Creates a value from an iterator."},{"DocComment":""},{"DocComment":" See the [module-level documentation] for more."},{"DocComment":""},{"DocComment":" [module-level documentation]: crate::iter"},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" let five_fives = std::iter::repeat(5).take(5);"},{"DocComment":""},{"DocComment":" let v = Vec::from_iter(five_fives);"},{"DocComment":""},{"DocComment":" assert_eq!(v, vec![5, 5, 5, 5, 5]);"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"from_iter_fn"},"generics":{"regions":[],"types":[{"index":0,"name":"Self"},{"index":1,"name":"A"},{"index":2,"name":"T"},{"index":3,"name":"Clause1_IntoIter"}],"const_generics":[],"trait_clauses":[{"clause_id":0,"span":{"data":{"file_id":1,"beg":{"line":1,"col":0},"end":{"line":1,"col":0}},"generated_from_span":null},"origin":"WhereClauseOnFn","trait_":{"regions":[],"skip_binder":{"id":38,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}}},{"clause_id":1,"span":{"data":{"file_id":32,"beg":{"line":152,"col":20},"end":{"line":152,"col":42}},"generated_from_span":null},"origin":"WhereClauseOnFn","trait_":{"regions":[],"skip_binder":{"id":35,"generics":{"regions":[],"types":[{"Deduplicated":8348},{"Deduplicated":8295},{"HashConsedValue":[8468,{"TypeVar":{"Free":3}}]}],"const_generics":[],"trait_refs":[]}}}}],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8348}],"output":{"Deduplicated":8294}},"src":{"TraitDecl":{"trait_ref":{"id":38,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}},"item_id":{"Method":0},"has_default":false}},"is_global_initializer":null,"body":"Opaque"},{"def_id":259,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["ops",0]},{"Ident":["try_trait",0]},{"Ident":["Try",0]},{"Ident":["from_output",0]}],"span":{"data":{"file_id":52,"beg":{"line":192,"col":4},"end":{"line":192,"col":49}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" Constructs the type from its `Output` type."},{"DocComment":""},{"DocComment":" This should be implemented consistently with the `branch` method"},{"DocComment":" such that applying the `?` operator will get back the original value:"},{"DocComment":" `Try::from_output(x).branch() --> ControlFlow::Continue(x)`."},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" #![feature(try_trait_v2)]"},{"DocComment":" use std::ops::Try;"},{"DocComment":""},{"DocComment":" assert_eq!(<Result<_, String> as Try>::from_output(3), Ok(3));"},{"DocComment":" assert_eq!(<Option<_> as Try>::from_output(4), Some(4));"},{"DocComment":" assert_eq!("},{"DocComment":" <std::ops::ControlFlow<String, _> as Try>::from_output(5),"},{"DocComment":" std::ops::ControlFlow::Continue(5),"},{"DocComment":" );"},{"DocComment":""},{"DocComment":" # fn make_question_mark_work() -> Option<()> {"},{"DocComment":" assert_eq!(Option::from_output(4)?, 4);"},{"DocComment":" # None }"},{"DocComment":" # make_question_mark_work();"},{"DocComment":""},{"DocComment":" // This is used, for example, on the accumulator in `try_fold`:"},{"DocComment":" let r = std::iter::empty().try_fold(4, |_, ()| -> Option<_> { unreachable!() });"},{"DocComment":" assert_eq!(r, Some(4));"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"from_output"},"generics":{"regions":[],"types":[{"index":0,"name":"Self"}],"const_generics":[],"trait_clauses":[{"clause_id":0,"span":{"data":{"file_id":1,"beg":{"line":1,"col":0},"end":{"line":1,"col":0}},"generated_from_span":null},"origin":"WhereClauseOnFn","trait_":{"regions":[],"skip_binder":{"id":39,"generics":{"regions":[],"types":[{"Deduplicated":8294}],"const_generics":[],"trait_refs":[]}}}}],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"HashConsedValue":[8470,{"TraitType":[{"HashConsedValue":[8469,{"kind":{"Clause":{"Free":0}},"trait_decl_ref":{"regions":[],"skip_binder":{"id":39,"generics":{"regions":[],"types":[{"Deduplicated":8294}],"const_generics":[],"trait_refs":[]}}}}]},0,{"regions":[],"types":[],"const_generics":[],"trait_refs":[]}]}]}],"output":{"Deduplicated":8294}},"src":{"TraitDecl":{"trait_ref":{"id":39,"generics":{"regions":[],"types":[{"Deduplicated":8294}],"const_generics":[],"trait_refs":[]}},"item_id":{"Method":0},"has_default":false}},"is_global_initializer":null,"body":"Opaque"},{"def_id":260,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["ops",0]},{"Ident":["try_trait",0]},{"Ident":["Try",0]},{"Ident":["branch",0]}],"span":{"data":{"file_id":52,"beg":{"line":219,"col":4},"end":{"line":219,"col":65}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" Used in `?` to decide whether the operator should produce a value"},{"DocComment":" (because this returned [`ControlFlow::Continue`])"},{"DocComment":" or propagate a value back to the caller"},{"DocComment":" (because this returned [`ControlFlow::Break`])."},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" #![feature(try_trait_v2)]"},{"DocComment":" use std::ops::{ControlFlow, Try};"},{"DocComment":""},{"DocComment":" assert_eq!(Ok::<_, String>(3).branch(), ControlFlow::Continue(3));"},{"DocComment":" assert_eq!(Err::<String, _>(3).branch(), ControlFlow::Break(Err(3)));"},{"DocComment":""},{"DocComment":" assert_eq!(Some(3).branch(), ControlFlow::Continue(3));"},{"DocComment":" assert_eq!(None::<String>.branch(), ControlFlow::Break(None));"},{"DocComment":""},{"DocComment":" assert_eq!(ControlFlow::<String, _>::Continue(3).branch(), ControlFlow::Continue(3));"},{"DocComment":" assert_eq!("},{"DocComment":" ControlFlow::<_, String>::Break(3).branch(),"},{"DocComment":" ControlFlow::Break(ControlFlow::Break(3)),"},{"DocComment":" );"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"branch"},"generics":{"regions":[],"types":[{"index":0,"name":"Self"}],"const_generics":[],"trait_clauses":[{"clause_id":0,"span":{"data":{"file_id":1,"beg":{"line":1,"col":0},"end":{"line":1,"col":0}},"generated_from_span":null},"origin":"WhereClauseOnFn","trait_":{"regions":[],"skip_binder":{"id":39,"generics":{"regions":[],"types":[{"Deduplicated":8294}],"const_generics":[],"trait_refs":[]}}}}],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8294}],"output":{"HashConsedValue":[8472,{"Adt":{"id":{"Adt":6},"generics":{"regions":[],"types":[{"HashConsedValue":[8471,{"TraitType":[{"Deduplicated":8469},1,{"regions":[],"types":[],"const_generics":[],"trait_refs":[]}]}]},{"Deduplicated":8470}],"const_generics":[],"trait_refs":[]}}}]}},"src":{"TraitDecl":{"trait_ref":{"id":39,"generics":{"regions":[],"types":[{"Deduplicated":8294}],"const_generics":[],"trait_refs":[]}},"item_id":{"Method":1},"has_default":false}},"is_global_initializer":null,"body":"Opaque"},{"def_id":261,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["iter",0]},{"Ident":["traits",0]},{"Ident":["collect",0]},{"Ident":["Extend",0]},{"Ident":["extend",0]}],"span":{"data":{"file_id":32,"beg":{"line":416,"col":4},"end":{"line":416,"col":61}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" Extends a collection with the contents of an iterator."},{"DocComment":""},{"DocComment":" As this is the only required method for this trait, the [trait-level] docs"},{"DocComment":" contain more details."},{"DocComment":""},{"DocComment":" [trait-level]: Extend"},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" // You can extend a String with some chars:"},{"DocComment":" let mut message = String::from(\"abc\");"},{"DocComment":""},{"DocComment":" message.extend(['d', 'e', 'f'].iter());"},{"DocComment":""},{"DocComment":" assert_eq!(\"abcdef\", &message);"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":null},"generics":{"regions":[{"index":0,"name":null,"mutability":"Unknown"}],"types":[{"index":0,"name":"Self"},{"index":1,"name":"A"},{"index":2,"name":"T"},{"index":3,"name":"Clause1_IntoIter"}],"const_generics":[],"trait_clauses":[{"clause_id":0,"span":{"data":{"file_id":1,"beg":{"line":1,"col":0},"end":{"line":1,"col":0}},"generated_from_span":null},"origin":"WhereClauseOnFn","trait_":{"regions":[],"skip_binder":{"id":41,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}}},{"clause_id":1,"span":{"data":{"file_id":32,"beg":{"line":416,"col":17},"end":{"line":416,"col":39}},"generated_from_span":null},"origin":"WhereClauseOnFn","trait_":{"regions":[],"skip_binder":{"id":35,"generics":{"regions":[],"types":[{"Deduplicated":8348},{"Deduplicated":8295},{"Deduplicated":8468}],"const_generics":[],"trait_refs":[]}}}}],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8451},{"Deduplicated":8348}],"output":{"Deduplicated":1108}},"src":{"TraitDecl":{"trait_ref":{"id":41,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}},"item_id":{"Method":0},"has_default":false}},"is_global_initializer":null,"body":"Opaque"},null,null,null,{"def_id":265,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["iter",0]},{"Ident":["traits",0]},{"Ident":["double_ended",0]},{"Ident":["DoubleEndedIterator",0]},{"Ident":["next_back",0]}],"span":{"data":{"file_id":53,"beg":{"line":96,"col":4},"end":{"line":96,"col":50}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" Removes and returns an element from the end of the iterator."},{"DocComment":""},{"DocComment":" Returns `None` when there are no more elements."},{"DocComment":""},{"DocComment":" The [trait-level] docs contain more details."},{"DocComment":""},{"DocComment":" [trait-level]: DoubleEndedIterator"},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" Basic usage:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" let numbers = vec![1, 2, 3, 4, 5, 6];"},{"DocComment":""},{"DocComment":" let mut iter = numbers.iter();"},{"DocComment":""},{"DocComment":" assert_eq!(Some(&1), iter.next());"},{"DocComment":" assert_eq!(Some(&6), iter.next_back());"},{"DocComment":" assert_eq!(Some(&5), iter.next_back());"},{"DocComment":" assert_eq!(Some(&2), iter.next());"},{"DocComment":" assert_eq!(Some(&3), iter.next());"},{"DocComment":" assert_eq!(Some(&4), iter.next());"},{"DocComment":" assert_eq!(None, iter.next());"},{"DocComment":" assert_eq!(None, iter.next_back());"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" # Remarks"},{"DocComment":""},{"DocComment":" The elements yielded by `DoubleEndedIterator`'s methods may differ from"},{"DocComment":" the ones yielded by [`Iterator`]'s methods:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" let vec = vec![(1, 'a'), (1, 'b'), (1, 'c'), (2, 'a'), (2, 'b')];"},{"DocComment":" let uniq_by_fst_comp = || {"},{"DocComment":" let mut seen = std::collections::HashSet::new();"},{"DocComment":" vec.iter().copied().filter(move |x| seen.insert(x.0))"},{"DocComment":" };"},{"DocComment":""},{"DocComment":" assert_eq!(uniq_by_fst_comp().last(), Some((2, 'a')));"},{"DocComment":" assert_eq!(uniq_by_fst_comp().next_back(), Some((2, 'b')));"},{"DocComment":""},{"DocComment":" assert_eq!("},{"DocComment":" uniq_by_fst_comp().fold(vec![], |mut v, x| {v.push(x); v}),"},{"DocComment":" vec![(1, 'a'), (2, 'a')]"},{"DocComment":" );"},{"DocComment":" assert_eq!("},{"DocComment":" uniq_by_fst_comp().rfold(vec![], |mut v, x| {v.push(x); v}),"},{"DocComment":" vec![(2, 'b'), (1, 'c')]"},{"DocComment":" );"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":null},"generics":{"regions":[{"index":0,"name":null,"mutability":"Unknown"}],"types":[{"index":0,"name":"Self"},{"index":1,"name":"Clause0_Clause0_Item"}],"const_generics":[],"trait_clauses":[{"clause_id":0,"span":{"data":{"file_id":1,"beg":{"line":1,"col":0},"end":{"line":1,"col":0}},"generated_from_span":null},"origin":"WhereClauseOnFn","trait_":{"regions":[],"skip_binder":{"id":42,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}}}],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8451}],"output":{"Deduplicated":8385}},"src":{"TraitDecl":{"trait_ref":{"id":42,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}},"item_id":{"Method":0},"has_default":false}},"is_global_initializer":null,"body":"Opaque"},null,null,null,null,null,null,null,null,null,null,{"def_id":276,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["num",0]},{"Impl":{"Ty":{"params":{"regions":[],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"Deduplicated":2226},"kind":"InherentImplBlock"}}},{"Ident":["wrapping_sub",0]}],"span":{"data":{"file_id":60,"beg":{"line":2620,"col":8},"end":{"line":2620,"col":58}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" 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GENERATOR;","attr_info":{"attributes":[],"inline":null,"rename":null,"public":true},"is_local":true,"opacity":"Transparent","lang_item":null},"generics":{"regions":[],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"ty":{"Deduplicated":1079},"src":{"TraitImpl":{"impl_ref":{"id":38,"generics":{"regions":[],"types":[],"const_generics":[],"trait_refs":[]}},"trait_ref":{"id":29,"generics":{"regions":[],"types":[{"Deduplicated":1079},{"Deduplicated":1895}],"const_generics":[],"trait_refs":[]}},"item_id":{"Const":4},"reuses_default":true}},"global_kind":"NamedConst","value":{"kind":{"Call":[{"kind":{"Fun":{"Regular":244}},"generics":{"regions":[],"types":[],"const_generics":[],"trait_refs":[]}},[]]},"ty":{"Deduplicated":1079}}},{"def_id":40,"item_meta":{"name":[{"Ident":["pasta_curves",0]},{"Ident":["fields",0]},{"Ident":["fp",0]},{"Impl":{"Trait":38}},{"Ident":["S",0]}],"span":{"data":{"file_id":2,"beg":{"line":634,"col":4},"end":{"line":634,"col":21}},"generated_from_span":null},"source_text":"const S: u32 = S;","attr_info":{"attributes":[],"inline":null,"rename":null,"public":true},"is_local":true,"opacity":"Transparent","lang_item":null},"generics":{"regions":[],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"ty":{"Deduplicated":1834},"src":{"TraitImpl":{"impl_ref":{"id":38,"generics":{"regions":[],"types":[],"const_generics":[],"trait_refs":[]}},"trait_ref":{"id":29,"generics":{"regions":[],"types":[{"Deduplicated":1079},{"Deduplicated":1895}],"const_generics":[],"trait_refs":[]}},"item_id":{"Const":5},"reuses_default":true}},"global_kind":"NamedConst","value":{"kind":{"Call":[{"kind":{"Fun":{"Regular":245}},"generics":{"regions":[],"types":[],"const_generics":[],"trait_refs":[]}},[]]},"ty":{"Deduplicated":1834}}},{"def_id":41,"item_meta":{"name":[{"Ident":["pasta_curves",0]},{"Ident":["fields",0]},{"Ident":["fp",0]},{"Impl":{"Trait":38}},{"Ident":["ROOT_OF_UNITY",0]}],"span":{"data":{"file_id":2,"beg":{"line":635,"col":4},"end":{"line":635,"col":46}},"generated_from_span":null},"source_text":"const ROOT_OF_UNITY: Self = ROOT_OF_UNITY;","attr_info":{"attributes":[],"inline":null,"rename":null,"public":true},"is_local":true,"opacity":"Transparent","lang_item":null},"generics":{"regions":[],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"ty":{"Deduplicated":1079},"src":{"TraitImpl":{"impl_ref":{"id":38,"generics":{"regions":[],"types":[],"const_generics":[],"trait_refs":[]}},"trait_ref":{"id":29,"generics":{"regions":[],"types":[{"Deduplicated":1079},{"Deduplicated":1895}],"const_generics":[],"trait_refs":[]}},"item_id":{"Const":6},"reuses_default":true}},"global_kind":"NamedConst","value":{"kind":{"Call":[{"kind":{"Fun":{"Regular":246}},"generics":{"regions":[],"types":[],"const_generics":[],"trait_refs":[]}},[]]},"ty":{"Deduplicated":1079}}},{"def_id":42,"item_meta":{"name":[{"Ident":["pasta_curves",0]},{"Ident":["fields",0]},{"Ident":["fp",0]},{"Impl":{"Trait":38}},{"Ident":["ROOT_OF_UNITY_INV",0]}],"span":{"data":{"file_id":2,"beg":{"line":636,"col":4},"end":{"line":641,"col":7}},"generated_from_span":null},"source_text":"const ROOT_OF_UNITY_INV: Self = Fp::from_raw([\n 0xf0b87c7db2ce91f6,\n 0x84a0a1d8859f066f,\n 0xb4ed8e647196dad1,\n 0x2cd5282c53116b5c,\n ]);","attr_info":{"attributes":[],"inline":null,"rename":null,"public":true},"is_local":true,"opacity":"Transparent","lang_item":null},"generics":{"regions":[],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"ty":{"Deduplicated":1079},"src":{"TraitImpl":{"impl_ref":{"id":38,"generics":{"regions":[],"types":[],"const_generics":[],"trait_refs":[]}},"trait_ref":{"id":29,"generics":{"regions":[],"types":[{"Deduplicated":1079},{"Deduplicated":1895}],"const_generics":[],"trait_refs":[]}},"item_id":{"Const":7},"reuses_default":true}},"global_kind":"NamedConst","value":{"kind":{"Call":[{"kind":{"Fun":{"Regular":247}},"generics":{"regions":[],"types":[],"const_generics":[],"trait_refs":[]}},[]]},"ty":{"Deduplicated":1079}}},{"def_id":43,"item_meta":{"name":[{"Ident":["pasta_curves",0]},{"Ident":["fields",0]},{"Ident":["fp",0]},{"Impl":{"Trait":38}},{"Ident":["DELTA",0]}],"span":{"data":{"file_id":2,"beg":{"line":642,"col":4},"end":{"line":642,"col":30}},"generated_from_span":null},"source_text":"const DELTA: Self = DELTA;","attr_info":{"attributes":[],"inline":null,"rename":null,"public":true},"is_local":true,"opacity":"Transparent","lang_item":null},"generics":{"regions":[],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"ty":{"Deduplicated":1079},"src":{"TraitImpl":{"impl_ref":{"id":38,"generics":{"regions":[],"types":[],"const_generics":[],"trait_refs":[]}},"trait_ref":{"id":29,"generics":{"regions":[],"types":[{"Deduplicated":1079},{"Deduplicated":1895}],"const_generics":[],"trait_refs":[]}},"item_id":{"Const":8},"reuses_default":true}},"global_kind":"NamedConst","value":{"kind":{"Call":[{"kind":{"Fun":{"Regular":248}},"generics":{"regions":[],"types":[],"const_generics":[],"trait_refs":[]}},[]]},"ty":{"Deduplicated":1079}}},{"def_id":44,"item_meta":{"name":[{"Ident":["pasta_curves",0]},{"Ident":["fields",0]},{"Ident":["fp",0]},{"Impl":{"Trait":40}},{"Ident":["ZETA",0]}],"span":{"data":{"file_id":2,"beg":{"line":789,"col":4},"end":{"line":794,"col":7}},"generated_from_span":null},"source_text":"const ZETA: Self = Fp::from_raw([\n 0x1dad5ebdfdfe4ab9,\n 0x1d1f8bd237ad3149,\n 0x2caad5dc57aab1b0,\n 0x12ccca834acdba71,\n ]);","attr_info":{"attributes":[],"inline":null,"rename":null,"public":true},"is_local":true,"opacity":"Opaque","lang_item":null},"generics":{"regions":[],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"ty":{"Deduplicated":1079},"src":{"TraitImpl":{"impl_ref":{"id":40,"generics":{"regions":[],"types":[],"const_generics":[],"trait_refs":[]}},"trait_ref":{"id":32,"generics":{"regions":[],"types":[{"Deduplicated":1079},{"Deduplicated":1895}],"const_generics":[{"kind":{"Literal":{"Scalar":{"Unsigned":["U8","3"]}}},"ty":{"Deduplicated":1894}}],"trait_refs":[]}},"item_id":{"Const":0},"reuses_default":true}},"global_kind":"NamedConst","value":{"kind":{"Call":[{"kind":{"Fun":{"Regular":251}},"generics":{"regions":[],"types":[],"const_generics":[],"trait_refs":[]}},[]]},"ty":{"Deduplicated":1079}}},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"trait_decls":[null,{"def_id":1,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["clone",0]},{"Ident":["Clone",0]}],"span":{"data":{"file_id":4,"beg":{"line":194,"col":0},"end":{"line":194,"col":28}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" A common trait that allows explicit creation of a duplicate value."},{"DocComment":""},{"DocComment":" Calling [`clone`] always produces a new value."},{"DocComment":" However, for types that are references to other data (such as smart pointers or references),"},{"DocComment":" the new value may still point to the same underlying data, rather than duplicating it."},{"DocComment":" See [`Clone::clone`] for more details."},{"DocComment":""},{"DocComment":" This distinction is especially important when using `#[derive(Clone)]` on structs containing"},{"DocComment":" smart pointers like `Arc<Mutex<T>>` - the cloned struct will share mutable state with the"},{"DocComment":" original."},{"DocComment":""},{"DocComment":" Differs from [`Copy`] in that [`Copy`] is implicit and an inexpensive bit-wise copy, while"},{"DocComment":" `Clone` is always explicit and may or may not be expensive. [`Copy`] has no methods, so you"},{"DocComment":" cannot change its behavior, but when implementing `Clone`, the `clone` method you provide"},{"DocComment":" may run arbitrary code."},{"DocComment":""},{"DocComment":" Since `Clone` is a supertrait of [`Copy`], any type that implements `Copy` must also implement"},{"DocComment":" `Clone`."},{"DocComment":""},{"DocComment":" ## Derivable"},{"DocComment":""},{"DocComment":" This trait can be used with `#[derive]` if all fields are `Clone`. The `derive`d"},{"DocComment":" implementation of [`Clone`] calls [`clone`] on each field."},{"DocComment":""},{"DocComment":" [`clone`]: Clone::clone"},{"DocComment":""},{"DocComment":" For a generic struct, `#[derive]` implements `Clone` conditionally by adding bound `Clone` on"},{"DocComment":" generic parameters."},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" // `derive` implements Clone for Reading<T> when T is Clone."},{"DocComment":" #[derive(Clone)]"},{"DocComment":" struct Reading<T> {"},{"DocComment":" frequency: T,"},{"DocComment":" }"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" ## How can I implement `Clone`?"},{"DocComment":""},{"DocComment":" Types that are [`Copy`] should have a trivial implementation of `Clone`. More formally:"},{"DocComment":" if `T: Copy`, `x: T`, and `y: &T`, then `let x = y.clone();` is equivalent to `let x = *y;`."},{"DocComment":" Manual implementations should be careful to uphold this invariant; however, unsafe code"},{"DocComment":" must not rely on it to ensure memory safety."},{"DocComment":""},{"DocComment":" An example is a generic struct holding a function pointer. In this case, the"},{"DocComment":" implementation of `Clone` cannot be `derive`d, but can be implemented as:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" struct Generate<T>(fn() -> T);"},{"DocComment":""},{"DocComment":" impl<T> Copy for Generate<T> {}"},{"DocComment":""},{"DocComment":" impl<T> Clone for Generate<T> {"},{"DocComment":" fn clone(&self) -> Self {"},{"DocComment":" *self"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" If we `derive`:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" #[derive(Copy, Clone)]"},{"DocComment":" struct Generate<T>(fn() -> T);"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" the auto-derived implementations will have unnecessary `T: Copy` and `T: Clone` bounds:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" # struct Generate<T>(fn() -> T);"},{"DocComment":""},{"DocComment":" // Automatically derived"},{"DocComment":" impl<T: Copy> Copy for Generate<T> { }"},{"DocComment":""},{"DocComment":" // Automatically derived"},{"DocComment":" impl<T: Clone> Clone for Generate<T> {"},{"DocComment":" fn clone(&self) -> Generate<T> {"},{"DocComment":" Generate(Clone::clone(&self.0))"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" The bounds are unnecessary because clearly the function itself should be"},{"DocComment":" copy- and cloneable even if its return type is not:"},{"DocComment":""},{"DocComment":" ```compile_fail,E0599"},{"DocComment":" #[derive(Copy, Clone)]"},{"DocComment":" struct Generate<T>(fn() -> T);"},{"DocComment":""},{"DocComment":" struct NotCloneable;"},{"DocComment":""},{"DocComment":" fn generate_not_cloneable() -> NotCloneable {"},{"DocComment":" NotCloneable"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" Generate(generate_not_cloneable).clone(); // error: trait bounds were not satisfied"},{"DocComment":" // Note: With the manual implementations the above line will compile."},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" ## `Clone` and `PartialEq`/`Eq`"},{"DocComment":" `Clone` is intended for the duplication of objects. Consequently, when implementing"},{"DocComment":" both `Clone` and [`PartialEq`], the following property is expected to hold:"},{"DocComment":" ```text"},{"DocComment":" x == x -> x.clone() == x"},{"DocComment":" ```"},{"DocComment":" In other words, if an object compares equal to itself,"},{"DocComment":" its clone must also compare equal to the original."},{"DocComment":""},{"DocComment":" For types that also implement [`Eq`] – for which `x == x` always holds –"},{"DocComment":" this implies that `x.clone() == x` must always be true."},{"DocComment":" Standard library collections such as"},{"DocComment":" [`HashMap`], [`HashSet`], [`BTreeMap`], [`BTreeSet`] and [`BinaryHeap`]"},{"DocComment":" rely on their keys respecting this property for correct behavior."},{"DocComment":" Furthermore, these collections require that cloning a key preserves the outcome of the"},{"DocComment":" [`Hash`] and [`Ord`] methods. Thankfully, this follows automatically from `x.clone() == x`"},{"DocComment":" if `Hash` and `Ord` are correctly implemented according to their own requirements."},{"DocComment":""},{"DocComment":" When deriving both `Clone` and [`PartialEq`] using `#[derive(Clone, PartialEq)]`"},{"DocComment":" or when additionally deriving [`Eq`] using `#[derive(Clone, PartialEq, Eq)]`,"},{"DocComment":" then this property is automatically upheld – provided that it is satisfied by"},{"DocComment":" the underlying types."},{"DocComment":""},{"DocComment":" Violating this property is a logic error. The behavior resulting from a logic error is not"},{"DocComment":" specified, but users of the trait must ensure that such logic errors do *not* result in"},{"DocComment":" undefined behavior. This means that `unsafe` code **must not** rely on this property"},{"DocComment":" being satisfied."},{"DocComment":""},{"DocComment":" ## Additional implementors"},{"DocComment":""},{"DocComment":" In addition to the [implementors listed below][impls],"},{"DocComment":" the following types also implement `Clone`:"},{"DocComment":""},{"DocComment":" * Function item types (i.e., the distinct types defined for each function)"},{"DocComment":" * Function pointer types (e.g., `fn() -> i32`)"},{"DocComment":" * Closure types, if they capture no value from the environment"},{"DocComment":" or if all such captured values implement `Clone` themselves."},{"DocComment":" Note that variables captured by shared reference always implement `Clone`"},{"DocComment":" (even if the referent doesn't),"},{"DocComment":" while variables captured by mutable reference never implement `Clone`."},{"DocComment":""},{"DocComment":" [`HashMap`]: ../../std/collections/struct.HashMap.html"},{"DocComment":" [`HashSet`]: ../../std/collections/struct.HashSet.html"},{"DocComment":" [`BTreeMap`]: ../../std/collections/struct.BTreeMap.html"},{"DocComment":" [`BTreeSet`]: ../../std/collections/struct.BTreeSet.html"},{"DocComment":" [`BinaryHeap`]: ../../std/collections/struct.BinaryHeap.html"},{"DocComment":" [impls]: #implementors"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"clone"},"generics":{"regions":[],"types":[{"index":0,"name":"Self"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[],"consts":[],"types":[],"methods":[{"params":{"regions":[{"index":0,"name":null,"mutability":"Unknown"}],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"clone","attr_info":{"attributes":[{"DocComment":" Returns a duplicate of the value."},{"DocComment":""},{"DocComment":" Note that what \"duplicate\" means varies by type:"},{"DocComment":" - For most types, this creates a deep, independent copy"},{"DocComment":" - For reference types like `&T`, this creates another reference to the same value"},{"DocComment":" - For smart pointers like [`Arc`] or [`Rc`], this increments the reference count"},{"DocComment":" but still points to the same underlying data"},{"DocComment":""},{"DocComment":" [`Arc`]: ../../std/sync/struct.Arc.html"},{"DocComment":" [`Rc`]: ../../std/rc/struct.Rc.html"},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" # #![allow(noop_method_call)]"},{"DocComment":" let hello = \"Hello\"; // &str implements Clone"},{"DocComment":""},{"DocComment":" assert_eq!(\"Hello\", hello.clone());"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" Example with a reference-counted type:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" use std::sync::{Arc, Mutex};"},{"DocComment":""},{"DocComment":" let data = Arc::new(Mutex::new(vec![1, 2, 3]));"},{"DocComment":" let data_clone = data.clone(); // Creates another Arc pointing to the same Mutex"},{"DocComment":""},{"DocComment":" {"},{"DocComment":" let mut lock = data.lock().unwrap();"},{"DocComment":" lock.push(4);"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" // Changes are visible through the clone because they share the same underlying data"},{"DocComment":" assert_eq!(*data_clone.lock().unwrap(), vec![1, 2, 3, 4]);"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"HashConsedValue":[8361,{"Ref":[{"Var":{"Bound":[0,0]}},{"Deduplicated":8294},"Shared"]}]}],"output":{"Deduplicated":8294}},"item":{"id":1,"generics":{"regions":[{"Var":{"Bound":[0,0]}}],"types":[{"Deduplicated":8294}],"const_generics":[],"trait_refs":[{"HashConsedValue":[8362,{"kind":"SelfId","trait_decl_ref":{"regions":[],"skip_binder":{"id":1,"generics":{"regions":[],"types":[{"Deduplicated":8294}],"const_generics":[],"trait_refs":[]}}}}]}]}}},"kind":{"TraitMethod":[1,0]}},null],"vtable":null},{"def_id":2,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["marker",0]},{"Ident":["Destruct",0]}],"span":{"data":{"file_id":6,"beg":{"line":1062,"col":0},"end":{"line":1062,"col":38}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" A marker for types that can be dropped."},{"DocComment":""},{"DocComment":" This should be used for `[const]` bounds,"},{"DocComment":" as non-const bounds will always hold for every type."}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"destruct"},"generics":{"regions":[],"types":[{"index":0,"name":"Self"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[],"consts":[],"types":[],"methods":[{"params":{"regions":[{"index":0,"name":null,"mutability":"Unknown"}],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"drop_glue","attr_info":{"attributes":[],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":true,"abi":"Rust","inputs":[{"HashConsedValue":[8363,{"Ref":[{"Var":{"Bound":[0,0]}},{"Deduplicated":8294},"Mut"]}]}],"output":{"Deduplicated":1108}},"item":{"id":115,"generics":{"regions":[{"Var":{"Bound":[0,0]}}],"types":[{"Deduplicated":8294}],"const_generics":[],"trait_refs":[]}}},"kind":{"TraitMethod":[2,0]}}],"vtable":null},{"def_id":3,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["marker",0]},{"Ident":["Copy",0]}],"span":{"data":{"file_id":6,"beg":{"line":454,"col":0},"end":{"line":454,"col":21}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" Types whose values can be duplicated simply by copying bits."},{"DocComment":""},{"DocComment":" By default, variable bindings have 'move semantics.' In other"},{"DocComment":" words:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" #[derive(Debug)]"},{"DocComment":" struct Foo;"},{"DocComment":""},{"DocComment":" let x = Foo;"},{"DocComment":""},{"DocComment":" let y = x;"},{"DocComment":""},{"DocComment":" // `x` has moved into `y`, and so cannot be used"},{"DocComment":""},{"DocComment":" // println!(\"{x:?}\"); // error: use of moved value"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" However, if a type implements `Copy`, it instead has 'copy semantics':"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" // We can derive a `Copy` implementation. `Clone` is also required, as it's"},{"DocComment":" // a supertrait of `Copy`."},{"DocComment":" #[derive(Debug, Copy, Clone)]"},{"DocComment":" struct Foo;"},{"DocComment":""},{"DocComment":" let x = Foo;"},{"DocComment":""},{"DocComment":" let y = x;"},{"DocComment":""},{"DocComment":" // `y` is a copy of `x`"},{"DocComment":""},{"DocComment":" println!(\"{x:?}\"); // A-OK!"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" It's important to note that in these two examples, the only difference is whether you"},{"DocComment":" are allowed to access `x` after the assignment. Under the hood, both a copy and a move"},{"DocComment":" can result in bits being copied in memory, although this is sometimes optimized away."},{"DocComment":""},{"DocComment":" ## How can I implement `Copy`?"},{"DocComment":""},{"DocComment":" There are two ways to implement `Copy` on your type. The simplest is to use `derive`:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" #[derive(Copy, Clone)]"},{"DocComment":" struct MyStruct;"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" You can also implement `Copy` and `Clone` manually:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" struct MyStruct;"},{"DocComment":""},{"DocComment":" impl Copy for MyStruct { }"},{"DocComment":""},{"DocComment":" impl Clone for MyStruct {"},{"DocComment":" fn clone(&self) -> MyStruct {"},{"DocComment":" *self"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" There is a small difference between the two. The `derive` strategy will also place a `Copy`"},{"DocComment":" bound on type parameters:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" #[derive(Clone)]"},{"DocComment":" struct MyStruct<T>(T);"},{"DocComment":""},{"DocComment":" impl<T: Copy> Copy for MyStruct<T> { }"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" This isn't always desired. For example, shared references (`&T`) can be copied regardless of"},{"DocComment":" whether `T` is `Copy`. Likewise, a generic struct containing markers such as [`PhantomData`]"},{"DocComment":" could potentially be duplicated with a bit-wise copy."},{"DocComment":""},{"DocComment":" ## What's the difference between `Copy` and `Clone`?"},{"DocComment":""},{"DocComment":" Copies happen implicitly, for example as part of an assignment `y = x`. The behavior of"},{"DocComment":" `Copy` is not overloadable; it is always a simple bit-wise copy."},{"DocComment":""},{"DocComment":" Cloning is an explicit action, `x.clone()`. The implementation of [`Clone`] can"},{"DocComment":" provide any type-specific behavior necessary to duplicate values safely. For example,"},{"DocComment":" the implementation of [`Clone`] for [`String`] needs to copy the pointed-to string"},{"DocComment":" buffer in the heap. A simple bitwise copy of [`String`] values would merely copy the"},{"DocComment":" pointer, leading to a double free down the line. For this reason, [`String`] is [`Clone`]"},{"DocComment":" but not `Copy`."},{"DocComment":""},{"DocComment":" [`Clone`] is a supertrait of `Copy`, so everything which is `Copy` must also implement"},{"DocComment":" [`Clone`]. If a type is `Copy` then its [`Clone`] implementation only needs to return `*self`"},{"DocComment":" (see the example above)."},{"DocComment":""},{"DocComment":" ## When can my type be `Copy`?"},{"DocComment":""},{"DocComment":" A type can implement `Copy` if all of its components implement `Copy`. For example, this"},{"DocComment":" struct can be `Copy`:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" # #[allow(dead_code)]"},{"DocComment":" #[derive(Copy, Clone)]"},{"DocComment":" struct Point {"},{"DocComment":" x: i32,"},{"DocComment":" y: i32,"},{"DocComment":" }"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" A struct can be `Copy`, and [`i32`] is `Copy`, therefore `Point` is eligible to be `Copy`."},{"DocComment":" By contrast, consider"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" # #![allow(dead_code)]"},{"DocComment":" # struct Point;"},{"DocComment":" struct PointList {"},{"DocComment":" points: Vec<Point>,"},{"DocComment":" }"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" The struct `PointList` cannot implement `Copy`, because [`Vec<T>`] is not `Copy`. If we"},{"DocComment":" attempt to derive a `Copy` implementation, we'll get an error:"},{"DocComment":""},{"DocComment":" ```text"},{"DocComment":" the trait `Copy` cannot be implemented for this type; field `points` does not implement `Copy`"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" Shared references (`&T`) are also `Copy`, so a type can be `Copy`, even when it holds"},{"DocComment":" shared references of types `T` that are *not* `Copy`. Consider the following struct,"},{"DocComment":" which can implement `Copy`, because it only holds a *shared reference* to our non-`Copy`"},{"DocComment":" type `PointList` from above:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" # #![allow(dead_code)]"},{"DocComment":" # struct PointList;"},{"DocComment":" #[derive(Copy, Clone)]"},{"DocComment":" struct PointListWrapper<'a> {"},{"DocComment":" point_list_ref: &'a PointList,"},{"DocComment":" }"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" ## When *can't* my type be `Copy`?"},{"DocComment":""},{"DocComment":" Some types can't be copied safely. For example, copying `&mut T` would create an aliased"},{"DocComment":" mutable reference. Copying [`String`] would duplicate responsibility for managing the"},{"DocComment":" [`String`]'s buffer, leading to a double free."},{"DocComment":""},{"DocComment":" Generalizing the latter case, any type implementing [`Drop`] can't be `Copy`, because it's"},{"DocComment":" managing some resource besides its own [`size_of::<T>`] bytes."},{"DocComment":""},{"DocComment":" If you try to implement `Copy` on a struct or enum containing non-`Copy` data, you will get"},{"DocComment":" the error [E0204]."},{"DocComment":""},{"DocComment":" [E0204]: ../../error_codes/E0204.html"},{"DocComment":""},{"DocComment":" ## When *should* my type be `Copy`?"},{"DocComment":""},{"DocComment":" Generally speaking, if your type _can_ implement `Copy`, it should. Keep in mind, though,"},{"DocComment":" that implementing `Copy` is part of the public API of your type. If the type might become"},{"DocComment":" non-`Copy` in the future, it could be prudent to omit the `Copy` implementation now, to"},{"DocComment":" avoid a breaking API change."},{"DocComment":""},{"DocComment":" ## Additional implementors"},{"DocComment":""},{"DocComment":" In addition to the [implementors listed below][impls],"},{"DocComment":" the following types also implement `Copy`:"},{"DocComment":""},{"DocComment":" * Function item types (i.e., the distinct types defined for each function)"},{"DocComment":" * Function pointer types (e.g., `fn() -> i32`)"},{"DocComment":" * Closure types, if they capture no value from the environment"},{"DocComment":" or if all such captured values implement `Copy` themselves."},{"DocComment":" Note that variables captured by shared reference always implement `Copy`"},{"DocComment":" (even if the referent doesn't),"},{"DocComment":" while variables captured by mutable reference never implement `Copy`."},{"DocComment":""},{"DocComment":" [`Vec<T>`]: ../../std/vec/struct.Vec.html"},{"DocComment":" [`String`]: ../../std/string/struct.String.html"},{"DocComment":" [`size_of::<T>`]: size_of"},{"DocComment":" [impls]: #implementors"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"copy"},"generics":{"regions":[],"types":[{"index":0,"name":"Self"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[{"clause_id":0,"span":{"data":{"file_id":6,"beg":{"line":454,"col":16},"end":{"line":454,"col":21}},"generated_from_span":null},"origin":"WhereClauseOnTrait","trait_":{"regions":[],"skip_binder":{"id":1,"generics":{"regions":[],"types":[{"Deduplicated":8294}],"const_generics":[],"trait_refs":[]}}}}],"consts":[],"types":[],"methods":[],"vtable":null},{"def_id":4,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["cmp",0]},{"Ident":["Eq",0]}],"span":{"data":{"file_id":7,"beg":{"line":338,"col":0},"end":{"line":338,"col":58}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" Trait for comparisons corresponding to [equivalence relations]("},{"DocComment":" https://en.wikipedia.org/wiki/Equivalence_relation)."},{"DocComment":""},{"DocComment":" The primary difference to [`PartialEq`] is the additional requirement for reflexivity. A type"},{"DocComment":" that implements [`PartialEq`] guarantees that for all `a`, `b` and `c`:"},{"DocComment":""},{"DocComment":" - symmetric: `a == b` implies `b == a`"},{"DocComment":" - transitive: `a == b` and `b == c` implies `a == c`"},{"DocComment":" - consistent: `a != b` if and only if `!(a == b)`"},{"DocComment":""},{"DocComment":" `Eq`, which builds on top of [`PartialEq`] also implies:"},{"DocComment":""},{"DocComment":" - reflexive: `a == a`"},{"DocComment":""},{"DocComment":" This property cannot be checked by the compiler, and therefore `Eq` is a trait without methods."},{"DocComment":""},{"DocComment":" Violating this property is a logic error. The behavior resulting from a logic error is not"},{"DocComment":" specified, but users of the trait must ensure that such logic errors do *not* result in"},{"DocComment":" undefined behavior. This means that `unsafe` code **must not** rely on the correctness of these"},{"DocComment":" methods."},{"DocComment":""},{"DocComment":" Floating point types such as [`f32`] and [`f64`] implement only [`PartialEq`] but *not* `Eq`"},{"DocComment":" because `NaN` != `NaN`."},{"DocComment":""},{"DocComment":" ## Derivable"},{"DocComment":""},{"DocComment":" This trait can be used with `#[derive]`. When `derive`d, because `Eq` has no extra methods, it"},{"DocComment":" is only informing the compiler that this is an equivalence relation rather than a partial"},{"DocComment":" equivalence relation. Note that the `derive` strategy requires all fields are `Eq`, which isn't"},{"DocComment":" always desired."},{"DocComment":""},{"DocComment":" ## How can I implement `Eq`?"},{"DocComment":""},{"DocComment":" If you cannot use the `derive` strategy, specify that your type implements `Eq`, which has no"},{"DocComment":" extra methods:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" enum BookFormat {"},{"DocComment":" Paperback,"},{"DocComment":" Hardback,"},{"DocComment":" Ebook,"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" struct Book {"},{"DocComment":" isbn: i32,"},{"DocComment":" format: BookFormat,"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl PartialEq for Book {"},{"DocComment":" fn eq(&self, other: &Self) -> bool {"},{"DocComment":" self.isbn == other.isbn"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl Eq for Book {}"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"Eq"},"generics":{"regions":[],"types":[{"index":0,"name":"Self"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[{"clause_id":0,"span":{"data":{"file_id":7,"beg":{"line":338,"col":20},"end":{"line":338,"col":43}},"generated_from_span":null},"origin":"WhereClauseOnTrait","trait_":{"regions":[],"skip_binder":{"id":5,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8294}],"const_generics":[],"trait_refs":[]}}}}],"consts":[],"types":[],"methods":[null,{"params":{"regions":[{"index":0,"name":null,"mutability":"Unknown"}],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"assert_fields_are_eq","attr_info":{"attributes":[],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8361}],"output":{"Deduplicated":1108}},"item":{"id":4,"generics":{"regions":[{"Var":{"Bound":[0,0]}}],"types":[{"Deduplicated":8294}],"const_generics":[],"trait_refs":[{"HashConsedValue":[8364,{"kind":"SelfId","trait_decl_ref":{"regions":[],"skip_binder":{"id":4,"generics":{"regions":[],"types":[{"Deduplicated":8294}],"const_generics":[],"trait_refs":[]}}}}]}]}}},"kind":{"TraitMethod":[4,1]}}],"vtable":null},{"def_id":5,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["cmp",0]},{"Ident":["PartialEq",0]}],"span":{"data":{"file_id":7,"beg":{"line":250,"col":0},"end":{"line":250,"col":65}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" Trait for comparisons using the equality operator."},{"DocComment":""},{"DocComment":" Implementing this trait for types provides the `==` and `!=` operators for"},{"DocComment":" those types."},{"DocComment":""},{"DocComment":" `x.eq(y)` can also be written `x == y`, and `x.ne(y)` can be written `x != y`."},{"DocComment":" We use the easier-to-read infix notation in the remainder of this documentation."},{"DocComment":""},{"DocComment":" This trait allows for comparisons using the equality operator, for types"},{"DocComment":" that do not have a full equivalence relation. For example, in floating point"},{"DocComment":" numbers `NaN != NaN`, so floating point types implement `PartialEq` but not"},{"DocComment":" [`trait@Eq`]. Formally speaking, when `Rhs == Self`, this trait corresponds"},{"DocComment":" to a [partial equivalence relation]."},{"DocComment":""},{"DocComment":" [partial equivalence relation]: https://en.wikipedia.org/wiki/Partial_equivalence_relation"},{"DocComment":""},{"DocComment":" Implementations must ensure that `eq` and `ne` are consistent with each other:"},{"DocComment":""},{"DocComment":" - `a != b` if and only if `!(a == b)`."},{"DocComment":""},{"DocComment":" The default implementation of `ne` provides this consistency and is almost"},{"DocComment":" always sufficient. It should not be overridden without very good reason."},{"DocComment":""},{"DocComment":" If [`PartialOrd`] or [`Ord`] are also implemented for `Self` and `Rhs`, their methods must also"},{"DocComment":" be consistent with `PartialEq` (see the documentation of those traits for the exact"},{"DocComment":" requirements). It's easy to accidentally make them disagree by deriving some of the traits and"},{"DocComment":" manually implementing others."},{"DocComment":""},{"DocComment":" The equality relation `==` must satisfy the following conditions"},{"DocComment":" (for all `a`, `b`, `c` of type `A`, `B`, `C`):"},{"DocComment":""},{"DocComment":" - **Symmetry**: if `A: PartialEq<B>` and `B: PartialEq<A>`, then **`a == b`"},{"DocComment":" implies `b == a`**; and"},{"DocComment":""},{"DocComment":" - **Transitivity**: if `A: PartialEq<B>` and `B: PartialEq<C>` and `A:"},{"DocComment":" PartialEq<C>`, then **`a == b` and `b == c` implies `a == c`**."},{"DocComment":" This must also work for longer chains, such as when `A: PartialEq<B>`, `B: PartialEq<C>`,"},{"DocComment":" `C: PartialEq<D>`, and `A: PartialEq<D>` all exist."},{"DocComment":""},{"DocComment":" Note that the `B: PartialEq<A>` (symmetric) and `A: PartialEq<C>`"},{"DocComment":" (transitive) impls are not forced to exist, but these requirements apply"},{"DocComment":" whenever they do exist."},{"DocComment":""},{"DocComment":" Violating these requirements is a logic error. The behavior resulting from a logic error is not"},{"DocComment":" specified, but users of the trait must ensure that such logic errors do *not* result in"},{"DocComment":" undefined behavior. This means that `unsafe` code **must not** rely on the correctness of these"},{"DocComment":" methods."},{"DocComment":""},{"DocComment":" ## Cross-crate considerations"},{"DocComment":""},{"DocComment":" Upholding the requirements stated above can become tricky when one crate implements `PartialEq`"},{"DocComment":" for a type of another crate (i.e., to allow comparing one of its own types with a type from the"},{"DocComment":" standard library). The recommendation is to never implement this trait for a foreign type. In"},{"DocComment":" other words, such a crate should do `impl PartialEq<ForeignType> for LocalType`, but it should"},{"DocComment":" *not* do `impl PartialEq<LocalType> for ForeignType`."},{"DocComment":""},{"DocComment":" This avoids the problem of transitive chains that criss-cross crate boundaries: for all local"},{"DocComment":" types `T`, you may assume that no other crate will add `impl`s that allow comparing `T == U`. In"},{"DocComment":" other words, if other crates add `impl`s that allow building longer transitive chains `U1 == ..."},{"DocComment":" == T == V1 == ...`, then all the types that appear to the right of `T` must be types that the"},{"DocComment":" crate defining `T` already knows about. This rules out transitive chains where downstream crates"},{"DocComment":" can add new `impl`s that \"stitch together\" comparisons of foreign types in ways that violate"},{"DocComment":" transitivity."},{"DocComment":""},{"DocComment":" Not having such foreign `impl`s also avoids forward compatibility issues where one crate adding"},{"DocComment":" more `PartialEq` implementations can cause build failures in downstream crates."},{"DocComment":""},{"DocComment":" ## Derivable"},{"DocComment":""},{"DocComment":" This trait can be used with `#[derive]`. When `derive`d on structs, two"},{"DocComment":" instances are equal if all fields are equal, and not equal if any fields"},{"DocComment":" are not equal. When `derive`d on enums, two instances are equal if they"},{"DocComment":" are the same variant and all fields are equal."},{"DocComment":""},{"DocComment":" ## How can I implement `PartialEq`?"},{"DocComment":""},{"DocComment":" An example implementation for a domain in which two books are considered"},{"DocComment":" the same book if their ISBN matches, even if the formats differ:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" enum BookFormat {"},{"DocComment":" Paperback,"},{"DocComment":" Hardback,"},{"DocComment":" Ebook,"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" struct Book {"},{"DocComment":" isbn: i32,"},{"DocComment":" format: BookFormat,"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl PartialEq for Book {"},{"DocComment":" fn eq(&self, other: &Self) -> bool {"},{"DocComment":" self.isbn == other.isbn"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" let b1 = Book { isbn: 3, format: BookFormat::Paperback };"},{"DocComment":" let b2 = Book { isbn: 3, format: BookFormat::Ebook };"},{"DocComment":" let b3 = Book { isbn: 10, format: BookFormat::Paperback };"},{"DocComment":""},{"DocComment":" assert!(b1 == b2);"},{"DocComment":" assert!(b1 != b3);"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" ## How can I compare two different types?"},{"DocComment":""},{"DocComment":" The type you can compare with is controlled by `PartialEq`'s type parameter."},{"DocComment":" For example, let's tweak our previous code a bit:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" // The derive implements <BookFormat> == <BookFormat> comparisons"},{"DocComment":" #[derive(PartialEq)]"},{"DocComment":" enum BookFormat {"},{"DocComment":" Paperback,"},{"DocComment":" Hardback,"},{"DocComment":" Ebook,"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" struct Book {"},{"DocComment":" isbn: i32,"},{"DocComment":" format: BookFormat,"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" // Implement <Book> == <BookFormat> comparisons"},{"DocComment":" impl PartialEq<BookFormat> for Book {"},{"DocComment":" fn eq(&self, other: &BookFormat) -> bool {"},{"DocComment":" self.format == *other"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" // Implement <BookFormat> == <Book> comparisons"},{"DocComment":" impl PartialEq<Book> for BookFormat {"},{"DocComment":" fn eq(&self, other: &Book) -> bool {"},{"DocComment":" *self == other.format"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" let b1 = Book { isbn: 3, format: BookFormat::Paperback };"},{"DocComment":""},{"DocComment":" assert!(b1 == BookFormat::Paperback);"},{"DocComment":" assert!(BookFormat::Ebook != b1);"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" By changing `impl PartialEq for Book` to `impl PartialEq<BookFormat> for Book`,"},{"DocComment":" we allow `BookFormat`s to be compared with `Book`s."},{"DocComment":""},{"DocComment":" A comparison like the one above, which ignores some fields of the struct,"},{"DocComment":" can be dangerous. It can easily lead to an unintended violation of the"},{"DocComment":" requirements for a partial equivalence relation. For example, if we kept"},{"DocComment":" the above implementation of `PartialEq<Book>` for `BookFormat` and added an"},{"DocComment":" implementation of `PartialEq<Book>` for `Book` (either via a `#[derive]` or"},{"DocComment":" via the manual implementation from the first example) then the result would"},{"DocComment":" violate transitivity:"},{"DocComment":""},{"DocComment":" ```should_panic"},{"DocComment":" #[derive(PartialEq)]"},{"DocComment":" enum BookFormat {"},{"DocComment":" Paperback,"},{"DocComment":" Hardback,"},{"DocComment":" Ebook,"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" #[derive(PartialEq)]"},{"DocComment":" struct Book {"},{"DocComment":" isbn: i32,"},{"DocComment":" format: BookFormat,"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl PartialEq<BookFormat> for Book {"},{"DocComment":" fn eq(&self, other: &BookFormat) -> bool {"},{"DocComment":" self.format == *other"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl PartialEq<Book> for BookFormat {"},{"DocComment":" fn eq(&self, other: &Book) -> bool {"},{"DocComment":" *self == other.format"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" fn main() {"},{"DocComment":" let b1 = Book { isbn: 1, format: BookFormat::Paperback };"},{"DocComment":" let b2 = Book { isbn: 2, format: BookFormat::Paperback };"},{"DocComment":""},{"DocComment":" assert!(b1 == BookFormat::Paperback);"},{"DocComment":" assert!(BookFormat::Paperback == b2);"},{"DocComment":""},{"DocComment":" // The following should hold by transitivity but doesn't."},{"DocComment":" assert!(b1 == b2); // <-- PANICS"},{"DocComment":" }"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" let x: u32 = 0;"},{"DocComment":" let y: u32 = 1;"},{"DocComment":""},{"DocComment":" assert_eq!(x == y, false);"},{"DocComment":" assert_eq!(x.eq(&y), false);"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" [`eq`]: PartialEq::eq"},{"DocComment":" [`ne`]: PartialEq::ne"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"eq"},"generics":{"regions":[],"types":[{"index":0,"name":"Self"},{"index":1,"name":"Rhs"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[],"consts":[],"types":[],"methods":[{"params":{"regions":[{"index":0,"name":null,"mutability":"Unknown"},{"index":1,"name":null,"mutability":"Unknown"}],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"eq","attr_info":{"attributes":[{"DocComment":" Tests for `self` and `other` values to be equal, and is used by `==`."}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8361},{"HashConsedValue":[8365,{"Ref":[{"Var":{"Bound":[0,1]}},{"Deduplicated":8295},"Shared"]}]}],"output":{"Deduplicated":1225}},"item":{"id":13,"generics":{"regions":[{"Var":{"Bound":[0,0]}},{"Var":{"Bound":[0,1]}}],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[{"HashConsedValue":[8366,{"kind":"SelfId","trait_decl_ref":{"regions":[],"skip_binder":{"id":5,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}}}]}]}}},"kind":{"TraitMethod":[5,0]}},null],"vtable":{"id":{"Adt":2},"generics":{"regions":[],"types":[{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}},{"def_id":6,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["fmt",0]},{"Ident":["Debug",0]}],"span":{"data":{"file_id":8,"beg":{"line":1053,"col":0},"end":{"line":1053,"col":29}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" `?` formatting."},{"DocComment":""},{"DocComment":" `Debug` should format the output in a programmer-facing, debugging context."},{"DocComment":""},{"DocComment":" Generally speaking, you should just `derive` a `Debug` implementation."},{"DocComment":""},{"DocComment":" When used with the alternate format specifier `#?`, the output is pretty-printed."},{"DocComment":""},{"DocComment":" For more information on formatters, see [the module-level documentation][module]."},{"DocComment":""},{"DocComment":" [module]: ../../std/fmt/index.html"},{"DocComment":""},{"DocComment":" This trait can be used with `#[derive]` if all fields implement `Debug`. When"},{"DocComment":" `derive`d for structs, it will use the name of the `struct`, then `{`, then a"},{"DocComment":" comma-separated list of each field's name and `Debug` value, then `}`. For"},{"DocComment":" `enum`s, it will use the name of the variant and, if applicable, `(`, then the"},{"DocComment":" `Debug` values of the fields, then `)`."},{"DocComment":""},{"DocComment":" # Stability"},{"DocComment":""},{"DocComment":" Derived `Debug` formats are not stable, and so may change with future Rust"},{"DocComment":" versions. Additionally, `Debug` implementations of types provided by the"},{"DocComment":" standard library (`std`, `core`, `alloc`, etc.) are not stable, and"},{"DocComment":" may also change with future Rust versions."},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" Deriving an implementation:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" #[derive(Debug)]"},{"DocComment":" struct Point {"},{"DocComment":" x: i32,"},{"DocComment":" y: i32,"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" let origin = Point { x: 0, y: 0 };"},{"DocComment":""},{"DocComment":" assert_eq!("},{"DocComment":" format!(\"The origin is: {origin:?}\"),"},{"DocComment":" \"The origin is: Point { x: 0, y: 0 }\","},{"DocComment":" );"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" Manually implementing:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" use std::fmt;"},{"DocComment":""},{"DocComment":" struct Point {"},{"DocComment":" x: i32,"},{"DocComment":" y: i32,"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl fmt::Debug for Point {"},{"DocComment":" fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {"},{"DocComment":" f.debug_struct(\"Point\")"},{"DocComment":" .field(\"x\", &self.x)"},{"DocComment":" .field(\"y\", &self.y)"},{"DocComment":" .finish()"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" let origin = Point { x: 0, y: 0 };"},{"DocComment":""},{"DocComment":" assert_eq!("},{"DocComment":" format!(\"The origin is: {origin:?}\"),"},{"DocComment":" \"The origin is: Point { x: 0, y: 0 }\","},{"DocComment":" );"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" There are a number of helper methods on the [`Formatter`] struct to help you with manual"},{"DocComment":" implementations, such as [`debug_struct`]."},{"DocComment":""},{"DocComment":" [`debug_struct`]: Formatter::debug_struct"},{"DocComment":""},{"DocComment":" Types that do not wish to use the standard suite of debug representations"},{"DocComment":" provided by the `Formatter` trait (`debug_struct`, `debug_tuple`,"},{"DocComment":" `debug_list`, `debug_set`, `debug_map`) can do something totally custom by"},{"DocComment":" manually writing an arbitrary representation to the `Formatter`."},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" # use std::fmt;"},{"DocComment":" # struct Point {"},{"DocComment":" # x: i32,"},{"DocComment":" # y: i32,"},{"DocComment":" # }"},{"DocComment":" #"},{"DocComment":" impl fmt::Debug for Point {"},{"DocComment":" fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {"},{"DocComment":" write!(f, \"Point [{} {}]\", self.x, self.y)"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" `Debug` implementations using either `derive` or the debug builder API"},{"DocComment":" on [`Formatter`] support pretty-printing using the alternate flag: `{:#?}`."},{"DocComment":""},{"DocComment":" Pretty-printing with `#?`:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" #[derive(Debug)]"},{"DocComment":" struct Point {"},{"DocComment":" x: i32,"},{"DocComment":" y: i32,"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" let origin = Point { x: 0, y: 0 };"},{"DocComment":""},{"DocComment":" let expected = \"The origin is: Point {"},{"DocComment":" x: 0,"},{"DocComment":" y: 0,"},{"DocComment":" }\";"},{"DocComment":" assert_eq!(format!(\"The origin is: {origin:#?}\"), expected);"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"Debug"},"generics":{"regions":[],"types":[{"index":0,"name":"Self"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[],"consts":[],"types":[],"methods":[{"params":{"regions":[{"index":0,"name":null,"mutability":"Unknown"},{"index":1,"name":null,"mutability":"Unknown"},{"index":2,"name":null,"mutability":"Unknown"}],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"fmt","attr_info":{"attributes":[{"DocComment":"Formats the value using the given formatter.\n\n# Errors\n\nThis function should return [`Err`] if, and only if, the provided [`Formatter`] returns [`Err`].\nString formatting is considered an infallible operation; this function only\nreturns a [`Result`] because writing to the underlying stream might fail and it must\nprovide a way to propagate the fact that an error has occurred back up the stack.\n"},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" use std::fmt;"},{"DocComment":""},{"DocComment":" struct Position {"},{"DocComment":" longitude: f32,"},{"DocComment":" latitude: f32,"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl fmt::Debug for Position {"},{"DocComment":" fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {"},{"DocComment":" f.debug_tuple(\"\")"},{"DocComment":" .field(&self.longitude)"},{"DocComment":" .field(&self.latitude)"},{"DocComment":" .finish()"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" let position = Position { longitude: 1.987, latitude: 2.983 };"},{"DocComment":" assert_eq!(format!(\"{position:?}\"), \"(1.987, 2.983)\");"},{"DocComment":""},{"DocComment":" assert_eq!(format!(\"{position:#?}\"), \"("},{"DocComment":" 1.987,"},{"DocComment":" 2.983,"},{"DocComment":" )\");"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8361},{"HashConsedValue":[2346,{"Ref":[{"Var":{"Bound":[0,1]}},{"HashConsedValue":[2345,{"Adt":{"id":{"Adt":9},"generics":{"regions":[{"Var":{"Bound":[0,2]}}],"types":[],"const_generics":[],"trait_refs":[]}}}]},"Mut"]}]}],"output":{"Deduplicated":2348}},"item":{"id":116,"generics":{"regions":[{"Var":{"Bound":[0,0]}},{"Var":{"Bound":[0,1]}},{"Var":{"Bound":[0,2]}}],"types":[{"Deduplicated":8294}],"const_generics":[],"trait_refs":[{"HashConsedValue":[8367,{"kind":"SelfId","trait_decl_ref":{"regions":[],"skip_binder":{"id":6,"generics":{"regions":[],"types":[{"Deduplicated":8294}],"const_generics":[],"trait_refs":[]}}}}]}]}}},"kind":{"TraitMethod":[6,0]}}],"vtable":{"id":{"Adt":8},"generics":{"regions":[],"types":[],"const_generics":[],"trait_refs":[]}}},{"def_id":7,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["convert",0]},{"Ident":["From",0]}],"span":{"data":{"file_id":9,"beg":{"line":587,"col":0},"end":{"line":587,"col":30}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" Used to do value-to-value conversions while consuming the input value. It is the reciprocal of"},{"DocComment":" [`Into`]."},{"DocComment":""},{"DocComment":" One should always prefer implementing `From` over [`Into`]"},{"DocComment":" because implementing `From` automatically provides one with an implementation of [`Into`]"},{"DocComment":" thanks to the blanket implementation in the standard library."},{"DocComment":""},{"DocComment":" Only implement [`Into`] when targeting a version prior to Rust 1.41 and converting to a type"},{"DocComment":" outside the current crate."},{"DocComment":" `From` was not able to do these types of conversions in earlier versions because of Rust's"},{"DocComment":" orphaning rules."},{"DocComment":" See [`Into`] for more details."},{"DocComment":""},{"DocComment":" Prefer using [`Into`] over [`From`] when specifying trait bounds on a generic function"},{"DocComment":" to ensure that types that only implement [`Into`] can be used as well."},{"DocComment":""},{"DocComment":" The `From` trait is also very useful when performing error handling. When constructing a function"},{"DocComment":" that is capable of failing, the return type will generally be of the form `Result<T, E>`."},{"DocComment":" `From` simplifies error handling by allowing a function to return a single error type"},{"DocComment":" that encapsulates multiple error types. See the \"Examples\" section and [the book][book] for more"},{"DocComment":" details."},{"DocComment":""},{"DocComment":" **Note: This trait must not fail**. The `From` trait is intended for perfect conversions."},{"DocComment":" If the conversion can fail or is not perfect, use [`TryFrom`]."},{"DocComment":""},{"DocComment":" # Generic Implementations"},{"DocComment":""},{"DocComment":" - `From<T> for U` implies [`Into`]`<U> for T`"},{"DocComment":" - `From` is reflexive, which means that `From<T> for T` is implemented"},{"DocComment":""},{"DocComment":" # When to implement `From`"},{"DocComment":""},{"DocComment":" While there's no technical restrictions on which conversions can be done using"},{"DocComment":" a `From` implementation, the general expectation is that the conversions"},{"DocComment":" should typically be restricted as follows:"},{"DocComment":""},{"DocComment":" * The conversion is *infallible*: if the conversion can fail, use [`TryFrom`]"},{"DocComment":" instead; don't provide a `From` impl that panics."},{"DocComment":""},{"DocComment":" * The conversion is *lossless*: semantically, it should not lose or discard"},{"DocComment":" information. For example, `i32: From<u16>` exists, where the original"},{"DocComment":" value can be recovered using `u16: TryFrom<i32>`. And `String: From<&str>`"},{"DocComment":" exists, where you can get something equivalent to the original value via"},{"DocComment":" `Deref`. But `From` cannot be used to convert from `u32` to `u16`, since"},{"DocComment":" that cannot succeed in a lossless way. (There's some wiggle room here for"},{"DocComment":" information not considered semantically relevant. For example,"},{"DocComment":" `Box<[T]>: From<Vec<T>>` exists even though it might not preserve capacity,"},{"DocComment":" like how two vectors can be equal despite differing capacities.)"},{"DocComment":""},{"DocComment":" * The conversion is *value-preserving*: the conceptual kind and meaning of"},{"DocComment":" the resulting value is the same, even though the Rust type and technical"},{"DocComment":" representation might be different. For example `-1_i8 as u8` is *lossless*,"},{"DocComment":" since `as` casting back can recover the original value, but that conversion"},{"DocComment":" is *not* available via `From` because `-1` and `255` are different conceptual"},{"DocComment":" values (despite being identical bit patterns technically). But"},{"DocComment":" `f32: From<i16>` *is* available because `1_i16` and `1.0_f32` are conceptually"},{"DocComment":" the same real number (despite having very different bit patterns technically)."},{"DocComment":" `String: From<char>` is available because they're both *text*, but"},{"DocComment":" `String: From<u32>` is *not* available, since `1` (a number) and `\"1\"`"},{"DocComment":" (text) are too different. (Converting values to text is instead covered"},{"DocComment":" by the [`Display`](crate::fmt::Display) trait.)"},{"DocComment":""},{"DocComment":" * The conversion is *obvious*: it's the only reasonable conversion between"},{"DocComment":" the two types. Otherwise it's better to have it be a named method or"},{"DocComment":" constructor, like how [`str::as_bytes`] is a method and how integers have"},{"DocComment":" methods like [`u32::from_ne_bytes`], [`u32::from_le_bytes`], and"},{"DocComment":" [`u32::from_be_bytes`], none of which are `From` implementations. Whereas"},{"DocComment":" there's only one reasonable way to wrap an [`Ipv6Addr`](crate::net::Ipv6Addr)"},{"DocComment":" into an [`IpAddr`](crate::net::IpAddr), thus `IpAddr: From<Ipv6Addr>` exists."},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" [`String`] implements `From<&str>`:"},{"DocComment":""},{"DocComment":" An explicit conversion from a `&str` to a String is done as follows:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" let string = \"hello\".to_string();"},{"DocComment":" let other_string = String::from(\"hello\");"},{"DocComment":""},{"DocComment":" assert_eq!(string, other_string);"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" While performing error handling it is often useful to implement `From` for your own error type."},{"DocComment":" By converting underlying error types to our own custom error type that encapsulates the"},{"DocComment":" underlying error type, we can return a single error type without losing information on the"},{"DocComment":" underlying cause. The '?' operator automatically converts the underlying error type to our"},{"DocComment":" custom error type with `From::from`."},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" use std::fs;"},{"DocComment":" use std::io;"},{"DocComment":" use std::num;"},{"DocComment":""},{"DocComment":" enum CliError {"},{"DocComment":" IoError(io::Error),"},{"DocComment":" ParseError(num::ParseIntError),"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl From<io::Error> for CliError {"},{"DocComment":" fn from(error: io::Error) -> Self {"},{"DocComment":" CliError::IoError(error)"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl From<num::ParseIntError> for CliError {"},{"DocComment":" fn from(error: num::ParseIntError) -> Self {"},{"DocComment":" CliError::ParseError(error)"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" fn open_and_parse_file(file_name: &str) -> Result<i32, CliError> {"},{"DocComment":" let mut contents = fs::read_to_string(&file_name)?;"},{"DocComment":" let num: i32 = contents.trim().parse()?;"},{"DocComment":" Ok(num)"},{"DocComment":" }"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" [`String`]: ../../std/string/struct.String.html"},{"DocComment":" [`from`]: From::from"},{"DocComment":" [book]: ../../book/ch09-00-error-handling.html"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"From"},"generics":{"regions":[],"types":[{"index":0,"name":"Self"},{"index":1,"name":"T"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[],"consts":[],"types":[],"methods":[{"params":{"regions":[],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"from","attr_info":{"attributes":[{"DocComment":" Converts to this type from the input type."}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8295}],"output":{"Deduplicated":8294}},"item":{"id":117,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[{"HashConsedValue":[8368,{"kind":"SelfId","trait_decl_ref":{"regions":[],"skip_binder":{"id":7,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}}}]}]}}},"kind":{"TraitMethod":[7,0]}}],"vtable":null},{"def_id":8,"item_meta":{"name":[{"Ident":["subtle",0]},{"Ident":["ConstantTimeEq",0]}],"span":{"data":{"file_id":10,"beg":{"line":262,"col":0},"end":{"line":262,"col":24}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" An `Eq`-like trait that produces a `Choice` instead of a `bool`."},{"DocComment":""},{"DocComment":" # Example"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" use subtle::ConstantTimeEq;"},{"DocComment":" let x: u8 = 5;"},{"DocComment":" let y: u8 = 13;"},{"DocComment":""},{"DocComment":" assert_eq!(x.ct_eq(&y).unwrap_u8(), 0);"},{"DocComment":" assert_eq!(x.ct_eq(&x).unwrap_u8(), 1);"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":null},"generics":{"regions":[],"types":[{"index":0,"name":"Self"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[],"consts":[],"types":[],"methods":[{"params":{"regions":[{"index":0,"name":null,"mutability":"Unknown"},{"index":1,"name":null,"mutability":"Unknown"}],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"ct_eq","attr_info":{"attributes":[{"DocComment":" Determine if two items are equal."},{"DocComment":""},{"DocComment":" The `ct_eq` function should execute in constant time."},{"DocComment":""},{"DocComment":" # Returns"},{"DocComment":""},{"DocComment":" * `Choice(1u8)` if `self == other`;"},{"DocComment":" * `Choice(0u8)` if `self != other`."}],"inline":"Hint","rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8361},{"HashConsedValue":[8369,{"Ref":[{"Var":{"Bound":[0,1]}},{"Deduplicated":8294},"Shared"]}]}],"output":{"Deduplicated":1250}},"item":{"id":10,"generics":{"regions":[{"Var":{"Bound":[0,0]}},{"Var":{"Bound":[0,1]}}],"types":[{"Deduplicated":8294}],"const_generics":[],"trait_refs":[{"HashConsedValue":[8370,{"kind":"SelfId","trait_decl_ref":{"regions":[],"skip_binder":{"id":8,"generics":{"regions":[],"types":[{"Deduplicated":8294}],"const_generics":[],"trait_refs":[]}}}}]}]}}},"kind":{"TraitMethod":[8,0]}},null],"vtable":null},{"def_id":9,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["cmp",0]},{"Ident":["Ord",0]}],"span":{"data":{"file_id":7,"beg":{"line":982,"col":0},"end":{"line":982,"col":73}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" Trait for types that form a [total order](https://en.wikipedia.org/wiki/Total_order)."},{"DocComment":""},{"DocComment":" Implementations must be consistent with the [`PartialOrd`] implementation, and ensure `max`,"},{"DocComment":" `min`, and `clamp` are consistent with `cmp`:"},{"DocComment":""},{"DocComment":" - `partial_cmp(a, b) == Some(cmp(a, b))`."},{"DocComment":" - `max(a, b) == max_by(a, b, cmp)` (ensured by the default implementation)."},{"DocComment":" - `min(a, b) == min_by(a, b, cmp)` (ensured by the default implementation)."},{"DocComment":" - For `a.clamp(min, max)`, see the [method docs](#method.clamp) (ensured by the default"},{"DocComment":" implementation)."},{"DocComment":""},{"DocComment":" Violating these requirements is a logic error. The behavior resulting from a logic error is not"},{"DocComment":" specified, but users of the trait must ensure that such logic errors do *not* result in"},{"DocComment":" undefined behavior. This means that `unsafe` code **must not** rely on the correctness of these"},{"DocComment":" methods."},{"DocComment":""},{"DocComment":" ## Corollaries"},{"DocComment":""},{"DocComment":" From the above and the requirements of `PartialOrd`, it follows that for all `a`, `b` and `c`:"},{"DocComment":""},{"DocComment":" - exactly one of `a < b`, `a == b` or `a > b` is true; and"},{"DocComment":" - `<` is transitive: `a < b` and `b < c` implies `a < c`. The same must hold for both `==` and"},{"DocComment":" `>`."},{"DocComment":""},{"DocComment":" Mathematically speaking, the `<` operator defines a strict [weak order]. In cases where `==`"},{"DocComment":" conforms to mathematical equality, it also defines a strict [total order]."},{"DocComment":""},{"DocComment":" [weak order]: https://en.wikipedia.org/wiki/Weak_ordering"},{"DocComment":" [total order]: https://en.wikipedia.org/wiki/Total_order"},{"DocComment":""},{"DocComment":" ## Derivable"},{"DocComment":""},{"DocComment":" This trait can be used with `#[derive]`."},{"DocComment":""},{"DocComment":" When `derive`d on structs, it will produce a"},{"DocComment":" [lexicographic](https://en.wikipedia.org/wiki/Lexicographic_order) ordering based on the"},{"DocComment":" top-to-bottom declaration order of the struct's members."},{"DocComment":""},{"DocComment":" When `derive`d on enums, variants are ordered primarily by their discriminants. Secondarily,"},{"DocComment":" they are ordered by their fields. By default, the discriminant is smallest for variants at the"},{"DocComment":" top, and largest for variants at the bottom. Here's an example:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" #[derive(PartialEq, Eq, PartialOrd, Ord)]"},{"DocComment":" enum E {"},{"DocComment":" Top,"},{"DocComment":" Bottom,"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" assert!(E::Top < E::Bottom);"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" However, manually setting the discriminants can override this default behavior:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" #[derive(PartialEq, Eq, PartialOrd, Ord)]"},{"DocComment":" enum E {"},{"DocComment":" Top = 2,"},{"DocComment":" Bottom = 1,"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" assert!(E::Bottom < E::Top);"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" ## Lexicographical comparison"},{"DocComment":""},{"DocComment":" Lexicographical comparison is an operation with the following properties:"},{"DocComment":" - Two sequences are compared element by element."},{"DocComment":" - The first mismatching element defines which sequence is lexicographically less or greater"},{"DocComment":" than the other."},{"DocComment":" - If one sequence is a prefix of another, the shorter sequence is lexicographically less than"},{"DocComment":" the other."},{"DocComment":" - If two sequences have equivalent elements and are of the same length, then the sequences are"},{"DocComment":" lexicographically equal."},{"DocComment":" - An empty sequence is lexicographically less than any non-empty sequence."},{"DocComment":" - Two empty sequences are lexicographically equal."},{"DocComment":""},{"DocComment":" ## How can I implement `Ord`?"},{"DocComment":""},{"DocComment":" `Ord` requires that the type also be [`PartialOrd`], [`PartialEq`], and [`Eq`]."},{"DocComment":""},{"DocComment":" Because `Ord` implies a stronger ordering relationship than [`PartialOrd`], and both `Ord` and"},{"DocComment":" [`PartialOrd`] must agree, you must choose how to implement `Ord` **first**. You can choose to"},{"DocComment":" derive it, or implement it manually. If you derive it, you should derive all four traits. If you"},{"DocComment":" implement it manually, you should manually implement all four traits, based on the"},{"DocComment":" implementation of `Ord`."},{"DocComment":""},{"DocComment":" Here's an example where you want to define the `Character` comparison by `health` and"},{"DocComment":" `experience` only, disregarding the field `mana`:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" use std::cmp::Ordering;"},{"DocComment":""},{"DocComment":" struct Character {"},{"DocComment":" health: u32,"},{"DocComment":" experience: u32,"},{"DocComment":" mana: f32,"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl Ord for Character {"},{"DocComment":" fn cmp(&self, other: &Self) -> Ordering {"},{"DocComment":" self.experience"},{"DocComment":" .cmp(&other.experience)"},{"DocComment":" .then(self.health.cmp(&other.health))"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl PartialOrd for Character {"},{"DocComment":" fn partial_cmp(&self, other: &Self) -> Option<Ordering> {"},{"DocComment":" Some(self.cmp(other))"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl PartialEq for Character {"},{"DocComment":" fn eq(&self, other: &Self) -> bool {"},{"DocComment":" self.health == other.health && self.experience == other.experience"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl Eq for Character {}"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" If all you need is to `slice::sort` a type by a field value, it can be simpler to use"},{"DocComment":" `slice::sort_by_key`."},{"DocComment":""},{"DocComment":" ## Examples of incorrect `Ord` implementations"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" use std::cmp::Ordering;"},{"DocComment":""},{"DocComment":" #[derive(Debug)]"},{"DocComment":" struct Character {"},{"DocComment":" health: f32,"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl Ord for Character {"},{"DocComment":" fn cmp(&self, other: &Self) -> std::cmp::Ordering {"},{"DocComment":" if self.health < other.health {"},{"DocComment":" Ordering::Less"},{"DocComment":" } else if self.health > other.health {"},{"DocComment":" Ordering::Greater"},{"DocComment":" } else {"},{"DocComment":" Ordering::Equal"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl PartialOrd for Character {"},{"DocComment":" fn partial_cmp(&self, other: &Self) -> Option<Ordering> {"},{"DocComment":" Some(self.cmp(other))"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl PartialEq for Character {"},{"DocComment":" fn eq(&self, other: &Self) -> bool {"},{"DocComment":" self.health == other.health"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl Eq for Character {}"},{"DocComment":""},{"DocComment":" let a = Character { health: 4.5 };"},{"DocComment":" let b = Character { health: f32::NAN };"},{"DocComment":""},{"DocComment":" // Mistake: floating-point values do not form a total order and using the built-in comparison"},{"DocComment":" // operands to implement `Ord` irregardless of that reality does not change it. Use"},{"DocComment":" // `f32::total_cmp` if you need a total order for floating-point values."},{"DocComment":""},{"DocComment":" // Reflexivity requirement of `Ord` is not given."},{"DocComment":" assert!(a == a);"},{"DocComment":" assert!(b != b);"},{"DocComment":""},{"DocComment":" // Antisymmetry requirement of `Ord` is not given. Only one of a < c and c < a is allowed to be"},{"DocComment":" // true, not both or neither."},{"DocComment":" assert_eq!((a < b) as u8 + (b < a) as u8, 0);"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" use std::cmp::Ordering;"},{"DocComment":""},{"DocComment":" #[derive(Debug)]"},{"DocComment":" struct Character {"},{"DocComment":" health: u32,"},{"DocComment":" experience: u32,"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl PartialOrd for Character {"},{"DocComment":" fn partial_cmp(&self, other: &Self) -> Option<Ordering> {"},{"DocComment":" Some(self.cmp(other))"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl Ord for Character {"},{"DocComment":" fn cmp(&self, other: &Self) -> std::cmp::Ordering {"},{"DocComment":" if self.health < 50 {"},{"DocComment":" self.health.cmp(&other.health)"},{"DocComment":" } else {"},{"DocComment":" self.experience.cmp(&other.experience)"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" // For performance reasons implementing `PartialEq` this way is not the idiomatic way, but it"},{"DocComment":" // ensures consistent behavior between `PartialEq`, `PartialOrd` and `Ord` in this example."},{"DocComment":" impl PartialEq for Character {"},{"DocComment":" fn eq(&self, other: &Self) -> bool {"},{"DocComment":" self.cmp(other) == Ordering::Equal"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl Eq for Character {}"},{"DocComment":""},{"DocComment":" let a = Character {"},{"DocComment":" health: 3,"},{"DocComment":" experience: 5,"},{"DocComment":" };"},{"DocComment":" let b = Character {"},{"DocComment":" health: 10,"},{"DocComment":" experience: 77,"},{"DocComment":" };"},{"DocComment":" let c = Character {"},{"DocComment":" health: 143,"},{"DocComment":" experience: 2,"},{"DocComment":" };"},{"DocComment":""},{"DocComment":" // Mistake: The implementation of `Ord` compares different fields depending on the value of"},{"DocComment":" // `self.health`, the resulting order is not total."},{"DocComment":""},{"DocComment":" // Transitivity requirement of `Ord` is not given. If a is smaller than b and b is smaller than"},{"DocComment":" // c, by transitive property a must also be smaller than c."},{"DocComment":" assert!(a < b && b < c && c < a);"},{"DocComment":""},{"DocComment":" // Antisymmetry requirement of `Ord` is not given. Only one of a < c and c < a is allowed to be"},{"DocComment":" // true, not both or neither."},{"DocComment":" assert_eq!((a < c) as u8 + (c < a) as u8, 2);"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" The documentation of [`PartialOrd`] contains further examples, for example it's wrong for"},{"DocComment":" [`PartialOrd`] and [`PartialEq`] to disagree."},{"DocComment":""},{"DocComment":" [`cmp`]: Ord::cmp"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"Ord"},"generics":{"regions":[],"types":[{"index":0,"name":"Self"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[{"clause_id":0,"span":{"data":{"file_id":7,"beg":{"line":982,"col":21},"end":{"line":982,"col":31}},"generated_from_span":null},"origin":"WhereClauseOnTrait","trait_":{"regions":[],"skip_binder":{"id":4,"generics":{"regions":[],"types":[{"Deduplicated":8294}],"const_generics":[],"trait_refs":[]}}}},{"clause_id":1,"span":{"data":{"file_id":7,"beg":{"line":982,"col":34},"end":{"line":982,"col":58}},"generated_from_span":null},"origin":"WhereClauseOnTrait","trait_":{"regions":[],"skip_binder":{"id":10,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8294}],"const_generics":[],"trait_refs":[]}}}}],"consts":[],"types":[],"methods":[{"params":{"regions":[{"index":0,"name":null,"mutability":"Unknown"},{"index":1,"name":null,"mutability":"Unknown"}],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"cmp","attr_info":{"attributes":[{"DocComment":" This method returns an [`Ordering`] between `self` and `other`."},{"DocComment":""},{"DocComment":" By convention, `self.cmp(&other)` returns the ordering matching the expression"},{"DocComment":" `self <operator> other` if true."},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" use std::cmp::Ordering;"},{"DocComment":""},{"DocComment":" assert_eq!(5.cmp(&10), Ordering::Less);"},{"DocComment":" assert_eq!(10.cmp(&5), Ordering::Greater);"},{"DocComment":" assert_eq!(5.cmp(&5), Ordering::Equal);"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8361},{"Deduplicated":8369}],"output":{"Deduplicated":1299}},"item":{"id":16,"generics":{"regions":[{"Var":{"Bound":[0,0]}},{"Var":{"Bound":[0,1]}}],"types":[{"Deduplicated":8294}],"const_generics":[],"trait_refs":[{"HashConsedValue":[8371,{"kind":"SelfId","trait_decl_ref":{"regions":[],"skip_binder":{"id":9,"generics":{"regions":[],"types":[{"Deduplicated":8294}],"const_generics":[],"trait_refs":[]}}}}]}]}}},"kind":{"TraitMethod":[9,0]}},null,null,null],"vtable":null},{"def_id":10,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["cmp",0]},{"Ident":["PartialOrd",0]}],"span":{"data":{"file_id":7,"beg":{"line":1366,"col":0},"end":{"line":1367,"col":41}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" Trait for types that form a [partial order](https://en.wikipedia.org/wiki/Partial_order)."},{"DocComment":""},{"DocComment":" The `lt`, `le`, `gt`, and `ge` methods of this trait can be called using the `<`, `<=`, `>`, and"},{"DocComment":" `>=` operators, respectively."},{"DocComment":""},{"DocComment":" This trait should **only** contain the comparison logic for a type **if one plans on only"},{"DocComment":" implementing `PartialOrd` but not [`Ord`]**. Otherwise the comparison logic should be in [`Ord`]"},{"DocComment":" and this trait implemented with `Some(self.cmp(other))`."},{"DocComment":""},{"DocComment":" The methods of this trait must be consistent with each other and with those of [`PartialEq`]."},{"DocComment":" The following conditions must hold:"},{"DocComment":""},{"DocComment":" 1. `a == b` if and only if `partial_cmp(a, b) == Some(Equal)`."},{"DocComment":" 2. `a < b` if and only if `partial_cmp(a, b) == Some(Less)`"},{"DocComment":" 3. `a > b` if and only if `partial_cmp(a, b) == Some(Greater)`"},{"DocComment":" 4. `a <= b` if and only if `a < b || a == b`"},{"DocComment":" 5. `a >= b` if and only if `a > b || a == b`"},{"DocComment":" 6. `a != b` if and only if `!(a == b)`."},{"DocComment":""},{"DocComment":" Conditions 2–5 above are ensured by the default implementation. Condition 6 is already ensured"},{"DocComment":" by [`PartialEq`]."},{"DocComment":""},{"DocComment":" If [`Ord`] is also implemented for `Self` and `Rhs`, it must also be consistent with"},{"DocComment":" `partial_cmp` (see the documentation of that trait for the exact requirements). It's easy to"},{"DocComment":" accidentally make them disagree by deriving some of the traits and manually implementing others."},{"DocComment":""},{"DocComment":" The comparison relations must satisfy the following conditions (for all `a`, `b`, `c` of type"},{"DocComment":" `A`, `B`, `C`):"},{"DocComment":""},{"DocComment":" - **Transitivity**: if `A: PartialOrd<B>` and `B: PartialOrd<C>` and `A: PartialOrd<C>`, then `a"},{"DocComment":" < b` and `b < c` implies `a < c`. The same must hold for both `==` and `>`. This must also"},{"DocComment":" work for longer chains, such as when `A: PartialOrd<B>`, `B: PartialOrd<C>`, `C:"},{"DocComment":" PartialOrd<D>`, and `A: PartialOrd<D>` all exist."},{"DocComment":" - **Duality**: if `A: PartialOrd<B>` and `B: PartialOrd<A>`, then `a < b` if and only if `b >"},{"DocComment":" a`."},{"DocComment":""},{"DocComment":" Note that the `B: PartialOrd<A>` (dual) and `A: PartialOrd<C>` (transitive) impls are not forced"},{"DocComment":" to exist, but these requirements apply whenever they do exist."},{"DocComment":""},{"DocComment":" Violating these requirements is a logic error. The behavior resulting from a logic error is not"},{"DocComment":" specified, but users of the trait must ensure that such logic errors do *not* result in"},{"DocComment":" undefined behavior. This means that `unsafe` code **must not** rely on the correctness of these"},{"DocComment":" methods."},{"DocComment":""},{"DocComment":" ## Cross-crate considerations"},{"DocComment":""},{"DocComment":" Upholding the requirements stated above can become tricky when one crate implements `PartialOrd`"},{"DocComment":" for a type of another crate (i.e., to allow comparing one of its own types with a type from the"},{"DocComment":" standard library). The recommendation is to never implement this trait for a foreign type. In"},{"DocComment":" other words, such a crate should do `impl PartialOrd<ForeignType> for LocalType`, but it should"},{"DocComment":" *not* do `impl PartialOrd<LocalType> for ForeignType`."},{"DocComment":""},{"DocComment":" This avoids the problem of transitive chains that criss-cross crate boundaries: for all local"},{"DocComment":" types `T`, you may assume that no other crate will add `impl`s that allow comparing `T < U`. In"},{"DocComment":" other words, if other crates add `impl`s that allow building longer transitive chains `U1 < ..."},{"DocComment":" < T < V1 < ...`, then all the types that appear to the right of `T` must be types that the crate"},{"DocComment":" defining `T` already knows about. This rules out transitive chains where downstream crates can"},{"DocComment":" add new `impl`s that \"stitch together\" comparisons of foreign types in ways that violate"},{"DocComment":" transitivity."},{"DocComment":""},{"DocComment":" Not having such foreign `impl`s also avoids forward compatibility issues where one crate adding"},{"DocComment":" more `PartialOrd` implementations can cause build failures in downstream crates."},{"DocComment":""},{"DocComment":" ## Corollaries"},{"DocComment":""},{"DocComment":" The following corollaries follow from the above requirements:"},{"DocComment":""},{"DocComment":" - irreflexivity of `<` and `>`: `!(a < a)`, `!(a > a)`"},{"DocComment":" - transitivity of `>`: if `a > b` and `b > c` then `a > c`"},{"DocComment":" - duality of `partial_cmp`: `partial_cmp(a, b) == partial_cmp(b, a).map(Ordering::reverse)`"},{"DocComment":""},{"DocComment":" ## Strict and non-strict partial orders"},{"DocComment":""},{"DocComment":" The `<` and `>` operators behave according to a *strict* partial order. However, `<=` and `>=`"},{"DocComment":" do **not** behave according to a *non-strict* partial order. That is because mathematically, a"},{"DocComment":" non-strict partial order would require reflexivity, i.e. `a <= a` would need to be true for"},{"DocComment":" every `a`. This isn't always the case for types that implement `PartialOrd`, for example:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" let a = f64::NAN;"},{"DocComment":" assert_eq!(a <= a, false);"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" ## Derivable"},{"DocComment":""},{"DocComment":" This trait can be used with `#[derive]`."},{"DocComment":""},{"DocComment":" When `derive`d on structs, it will produce a"},{"DocComment":" [lexicographic](https://en.wikipedia.org/wiki/Lexicographic_order) ordering based on the"},{"DocComment":" top-to-bottom declaration order of the struct's members."},{"DocComment":""},{"DocComment":" When `derive`d on enums, variants are primarily ordered by their discriminants. Secondarily,"},{"DocComment":" they are ordered by their fields. By default, the discriminant is smallest for variants at the"},{"DocComment":" top, and largest for variants at the bottom. Here's an example:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" #[derive(PartialEq, PartialOrd)]"},{"DocComment":" enum E {"},{"DocComment":" Top,"},{"DocComment":" Bottom,"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" assert!(E::Top < E::Bottom);"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" However, manually setting the discriminants can override this default behavior:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" #[derive(PartialEq, PartialOrd)]"},{"DocComment":" enum E {"},{"DocComment":" Top = 2,"},{"DocComment":" Bottom = 1,"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" assert!(E::Bottom < E::Top);"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" ## How can I implement `PartialOrd`?"},{"DocComment":""},{"DocComment":" `PartialOrd` only requires implementation of the [`partial_cmp`] method, with the others"},{"DocComment":" generated from default implementations."},{"DocComment":""},{"DocComment":" However it remains possible to implement the others separately for types which do not have a"},{"DocComment":" total order. For example, for floating point numbers, `NaN < 0 == false` and `NaN >= 0 == false`"},{"DocComment":" (cf. IEEE 754-2008 section 5.11)."},{"DocComment":""},{"DocComment":" `PartialOrd` requires your type to be [`PartialEq`]."},{"DocComment":""},{"DocComment":" If your type is [`Ord`], you can implement [`partial_cmp`] by using [`cmp`]:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" use std::cmp::Ordering;"},{"DocComment":""},{"DocComment":" struct Person {"},{"DocComment":" id: u32,"},{"DocComment":" name: String,"},{"DocComment":" height: u32,"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl PartialOrd for Person {"},{"DocComment":" fn partial_cmp(&self, other: &Self) -> Option<Ordering> {"},{"DocComment":" Some(self.cmp(other))"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl Ord for Person {"},{"DocComment":" fn cmp(&self, other: &Self) -> Ordering {"},{"DocComment":" self.height.cmp(&other.height)"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl PartialEq for Person {"},{"DocComment":" fn eq(&self, other: &Self) -> bool {"},{"DocComment":" self.height == other.height"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl Eq for Person {}"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" You may also find it useful to use [`partial_cmp`] on your type's fields. Here is an example of"},{"DocComment":" `Person` types who have a floating-point `height` field that is the only field to be used for"},{"DocComment":" sorting:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" use std::cmp::Ordering;"},{"DocComment":""},{"DocComment":" struct Person {"},{"DocComment":" id: u32,"},{"DocComment":" name: String,"},{"DocComment":" height: f64,"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl PartialOrd for Person {"},{"DocComment":" fn partial_cmp(&self, other: &Self) -> Option<Ordering> {"},{"DocComment":" self.height.partial_cmp(&other.height)"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl PartialEq for Person {"},{"DocComment":" fn eq(&self, other: &Self) -> bool {"},{"DocComment":" self.height == other.height"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" ## Examples of incorrect `PartialOrd` implementations"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" use std::cmp::Ordering;"},{"DocComment":""},{"DocComment":" #[derive(PartialEq, Debug)]"},{"DocComment":" struct Character {"},{"DocComment":" health: u32,"},{"DocComment":" experience: u32,"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl PartialOrd for Character {"},{"DocComment":" fn partial_cmp(&self, other: &Self) -> Option<Ordering> {"},{"DocComment":" Some(self.health.cmp(&other.health))"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" let a = Character {"},{"DocComment":" health: 10,"},{"DocComment":" experience: 5,"},{"DocComment":" };"},{"DocComment":" let b = Character {"},{"DocComment":" health: 10,"},{"DocComment":" experience: 77,"},{"DocComment":" };"},{"DocComment":""},{"DocComment":" // Mistake: `PartialEq` and `PartialOrd` disagree with each other."},{"DocComment":""},{"DocComment":" assert_eq!(a.partial_cmp(&b).unwrap(), Ordering::Equal); // a == b according to `PartialOrd`."},{"DocComment":" assert_ne!(a, b); // a != b according to `PartialEq`."},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" let x: u32 = 0;"},{"DocComment":" let y: u32 = 1;"},{"DocComment":""},{"DocComment":" assert_eq!(x < y, true);"},{"DocComment":" assert_eq!(x.lt(&y), true);"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" [`partial_cmp`]: PartialOrd::partial_cmp"},{"DocComment":" [`cmp`]: Ord::cmp"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"partial_ord"},"generics":{"regions":[],"types":[{"index":0,"name":"Self"},{"index":1,"name":"Rhs"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[{"clause_id":0,"span":{"data":{"file_id":7,"beg":{"line":1367,"col":4},"end":{"line":1367,"col":26}},"generated_from_span":null},"origin":"WhereClauseOnTrait","trait_":{"regions":[],"skip_binder":{"id":5,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}}}],"consts":[],"types":[],"methods":[{"params":{"regions":[{"index":0,"name":null,"mutability":"Unknown"},{"index":1,"name":null,"mutability":"Unknown"}],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"partial_cmp","attr_info":{"attributes":[{"DocComment":" This method returns an ordering between `self` and `other` values if one exists."},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" use std::cmp::Ordering;"},{"DocComment":""},{"DocComment":" let result = 1.0.partial_cmp(&2.0);"},{"DocComment":" assert_eq!(result, Some(Ordering::Less));"},{"DocComment":""},{"DocComment":" let result = 1.0.partial_cmp(&1.0);"},{"DocComment":" assert_eq!(result, Some(Ordering::Equal));"},{"DocComment":""},{"DocComment":" let result = 2.0.partial_cmp(&1.0);"},{"DocComment":" assert_eq!(result, Some(Ordering::Greater));"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" When comparison is impossible:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" let result = f64::NAN.partial_cmp(&1.0);"},{"DocComment":" assert_eq!(result, None);"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8361},{"Deduplicated":8365}],"output":{"Deduplicated":1352}},"item":{"id":21,"generics":{"regions":[{"Var":{"Bound":[0,0]}},{"Var":{"Bound":[0,1]}}],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[{"HashConsedValue":[8372,{"kind":"SelfId","trait_decl_ref":{"regions":[],"skip_binder":{"id":10,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}}}]}]}}},"kind":{"TraitMethod":[10,0]}},null,null,null,null,null,null,null,null],"vtable":{"id":{"Adt":4},"generics":{"regions":[],"types":[{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}},{"def_id":11,"item_meta":{"name":[{"Ident":["subtle",0]},{"Ident":["ConditionallySelectable",0]}],"span":{"data":{"file_id":10,"beg":{"line":393,"col":0},"end":{"line":393,"col":39}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" A type which can be conditionally selected in constant time."},{"DocComment":""},{"DocComment":" This trait also provides generic implementations of conditional"},{"DocComment":" assignment and conditional swaps."}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":null},"generics":{"regions":[],"types":[{"index":0,"name":"Self"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[{"clause_id":0,"span":{"data":{"file_id":10,"beg":{"line":393,"col":35},"end":{"line":393,"col":39}},"generated_from_span":null},"origin":"WhereClauseOnTrait","trait_":{"regions":[],"skip_binder":{"id":3,"generics":{"regions":[],"types":[{"Deduplicated":8294}],"const_generics":[],"trait_refs":[]}}}}],"consts":[],"types":[],"methods":[{"params":{"regions":[{"index":0,"name":null,"mutability":"Unknown"},{"index":1,"name":null,"mutability":"Unknown"}],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"conditional_select","attr_info":{"attributes":[{"DocComment":" Select `a` or `b` according to `choice`."},{"DocComment":""},{"DocComment":" # Returns"},{"DocComment":""},{"DocComment":" * `a` if `choice == Choice(0)`;"},{"DocComment":" * `b` if `choice == Choice(1)`."},{"DocComment":""},{"DocComment":" This function should execute in constant time."},{"DocComment":""},{"DocComment":" # Example"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" use subtle::ConditionallySelectable;"},{"DocComment":" #"},{"DocComment":" # fn main() {"},{"DocComment":" let x: u8 = 13;"},{"DocComment":" let y: u8 = 42;"},{"DocComment":""},{"DocComment":" let z = u8::conditional_select(&x, &y, 0.into());"},{"DocComment":" assert_eq!(z, x);"},{"DocComment":" let z = u8::conditional_select(&x, &y, 1.into());"},{"DocComment":" assert_eq!(z, y);"},{"DocComment":" # }"},{"DocComment":" ```"}],"inline":"Hint","rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8361},{"Deduplicated":8369},{"Deduplicated":1250}],"output":{"Deduplicated":8294}},"item":{"id":31,"generics":{"regions":[{"Var":{"Bound":[0,0]}},{"Var":{"Bound":[0,1]}}],"types":[{"Deduplicated":8294}],"const_generics":[],"trait_refs":[{"HashConsedValue":[8373,{"kind":"SelfId","trait_decl_ref":{"regions":[],"skip_binder":{"id":11,"generics":{"regions":[],"types":[{"Deduplicated":8294}],"const_generics":[],"trait_refs":[]}}}}]}]}}},"kind":{"TraitMethod":[11,0]}},null,null],"vtable":null},{"def_id":12,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["ops",0]},{"Ident":["arith",0]},{"Ident":["Neg",0]}],"span":{"data":{"file_id":14,"beg":{"line":690,"col":0},"end":{"line":690,"col":19}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" The unary negation operator `-`."},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" An implementation of `Neg` for `Sign`, which allows the use of `-` to"},{"DocComment":" negate its value."},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" use std::ops::Neg;"},{"DocComment":""},{"DocComment":" #[derive(Debug, PartialEq)]"},{"DocComment":" enum Sign {"},{"DocComment":" Negative,"},{"DocComment":" Zero,"},{"DocComment":" Positive,"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl Neg for Sign {"},{"DocComment":" type Output = Self;"},{"DocComment":""},{"DocComment":" fn neg(self) -> Self::Output {"},{"DocComment":" match self {"},{"DocComment":" Sign::Negative => Sign::Positive,"},{"DocComment":" Sign::Zero => Sign::Zero,"},{"DocComment":" Sign::Positive => Sign::Negative,"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" // A negative positive is a negative."},{"DocComment":" assert_eq!(-Sign::Positive, Sign::Negative);"},{"DocComment":" // A double negative is a positive."},{"DocComment":" assert_eq!(-Sign::Negative, Sign::Positive);"},{"DocComment":" // Zero is its own negation."},{"DocComment":" assert_eq!(-Sign::Zero, Sign::Zero);"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"neg"},"generics":{"regions":[],"types":[{"index":0,"name":"Self"},{"index":1,"name":"Self_Output"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[],"consts":[],"types":[null],"methods":[{"params":{"regions":[],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"neg","attr_info":{"attributes":[{"DocComment":" Performs the unary `-` operation."},{"DocComment":""},{"DocComment":" # Example"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" let x: i32 = 12;"},{"DocComment":" assert_eq!(-x, -12);"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8294}],"output":{"Deduplicated":8295}},"item":{"id":122,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[{"HashConsedValue":[8374,{"kind":"SelfId","trait_decl_ref":{"regions":[],"skip_binder":{"id":12,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}}}]}]}}},"kind":{"TraitMethod":[12,0]}}],"vtable":{"id":{"Adt":12},"generics":{"regions":[],"types":[{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}},{"def_id":13,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["ops",0]},{"Ident":["arith",0]},{"Ident":["Sub",0]}],"span":{"data":{"file_id":14,"beg":{"line":188,"col":0},"end":{"line":188,"col":31}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" The subtraction operator `-`."},{"DocComment":""},{"DocComment":" Note that `Rhs` is `Self` by default, but this is not mandatory. For"},{"DocComment":" example, [`std::time::SystemTime`] implements `Sub<Duration>`, which permits"},{"DocComment":" operations of the form `SystemTime = SystemTime - Duration`."},{"DocComment":""},{"DocComment":" [`std::time::SystemTime`]: ../../std/time/struct.SystemTime.html"},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" ## `Sub`tractable points"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" use std::ops::Sub;"},{"DocComment":""},{"DocComment":" #[derive(Debug, Copy, Clone, PartialEq)]"},{"DocComment":" struct Point {"},{"DocComment":" x: i32,"},{"DocComment":" y: i32,"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl Sub for Point {"},{"DocComment":" type Output = Self;"},{"DocComment":""},{"DocComment":" fn sub(self, other: Self) -> Self::Output {"},{"DocComment":" Self {"},{"DocComment":" x: self.x - other.x,"},{"DocComment":" y: self.y - other.y,"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" assert_eq!(Point { x: 3, y: 3 } - Point { x: 2, y: 3 },"},{"DocComment":" Point { x: 1, y: 0 });"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" ## Implementing `Sub` with generics"},{"DocComment":""},{"DocComment":" Here is an example of the same `Point` struct implementing the `Sub` trait"},{"DocComment":" using generics."},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" use std::ops::Sub;"},{"DocComment":""},{"DocComment":" #[derive(Debug, PartialEq)]"},{"DocComment":" struct Point<T> {"},{"DocComment":" x: T,"},{"DocComment":" y: T,"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" // Notice that the implementation uses the associated type `Output`."},{"DocComment":" impl<T: Sub<Output = T>> Sub for Point<T> {"},{"DocComment":" type Output = Self;"},{"DocComment":""},{"DocComment":" fn sub(self, other: Self) -> Self::Output {"},{"DocComment":" Point {"},{"DocComment":" x: self.x - other.x,"},{"DocComment":" y: self.y - other.y,"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" assert_eq!(Point { x: 2, y: 3 } - Point { x: 1, y: 0 },"},{"DocComment":" Point { x: 1, y: 3 });"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"sub"},"generics":{"regions":[],"types":[{"index":0,"name":"Self"},{"index":1,"name":"Rhs"},{"index":2,"name":"Self_Output"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[],"consts":[],"types":[null],"methods":[{"params":{"regions":[],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"sub","attr_info":{"attributes":[{"DocComment":" Performs the `-` operation."},{"DocComment":""},{"DocComment":" # Example"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" assert_eq!(12 - 1, 11);"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8294},{"Deduplicated":8295}],"output":{"Deduplicated":8348}},"item":{"id":123,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295},{"Deduplicated":8348}],"const_generics":[],"trait_refs":[{"HashConsedValue":[8375,{"kind":"SelfId","trait_decl_ref":{"regions":[],"skip_binder":{"id":13,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295},{"Deduplicated":8348}],"const_generics":[],"trait_refs":[]}}}}]}]}}},"kind":{"TraitMethod":[13,0]}}],"vtable":{"id":{"Adt":13},"generics":{"regions":[],"types":[{"Deduplicated":8295},{"Deduplicated":8348}],"const_generics":[],"trait_refs":[]}}},{"def_id":14,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["ops",0]},{"Ident":["arith",0]},{"Ident":["Add",0]}],"span":{"data":{"file_id":14,"beg":{"line":76,"col":0},"end":{"line":76,"col":31}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" The addition operator `+`."},{"DocComment":""},{"DocComment":" Note that `Rhs` is `Self` by default, but this is not mandatory. For"},{"DocComment":" example, [`std::time::SystemTime`] implements `Add<Duration>`, which permits"},{"DocComment":" operations of the form `SystemTime = SystemTime + Duration`."},{"DocComment":""},{"DocComment":" [`std::time::SystemTime`]: ../../std/time/struct.SystemTime.html"},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" ## `Add`able points"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" use std::ops::Add;"},{"DocComment":""},{"DocComment":" #[derive(Debug, Copy, Clone, PartialEq)]"},{"DocComment":" struct Point {"},{"DocComment":" x: i32,"},{"DocComment":" y: i32,"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl Add for Point {"},{"DocComment":" type Output = Self;"},{"DocComment":""},{"DocComment":" fn add(self, other: Self) -> Self {"},{"DocComment":" Self {"},{"DocComment":" x: self.x + other.x,"},{"DocComment":" y: self.y + other.y,"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" assert_eq!(Point { x: 1, y: 0 } + Point { x: 2, y: 3 },"},{"DocComment":" Point { x: 3, y: 3 });"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" ## Implementing `Add` with generics"},{"DocComment":""},{"DocComment":" Here is an example of the same `Point` struct implementing the `Add` trait"},{"DocComment":" using generics."},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" use std::ops::Add;"},{"DocComment":""},{"DocComment":" #[derive(Debug, Copy, Clone, PartialEq)]"},{"DocComment":" struct Point<T> {"},{"DocComment":" x: T,"},{"DocComment":" y: T,"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" // Notice that the implementation uses the associated type `Output`."},{"DocComment":" impl<T: Add<Output = T>> Add for Point<T> {"},{"DocComment":" type Output = Self;"},{"DocComment":""},{"DocComment":" fn add(self, other: Self) -> Self::Output {"},{"DocComment":" Self {"},{"DocComment":" x: self.x + other.x,"},{"DocComment":" y: self.y + other.y,"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" assert_eq!(Point { x: 1, y: 0 } + Point { x: 2, y: 3 },"},{"DocComment":" Point { x: 3, y: 3 });"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"add"},"generics":{"regions":[],"types":[{"index":0,"name":"Self"},{"index":1,"name":"Rhs"},{"index":2,"name":"Self_Output"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[],"consts":[],"types":[null],"methods":[{"params":{"regions":[],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"add","attr_info":{"attributes":[{"DocComment":" Performs the `+` operation."},{"DocComment":""},{"DocComment":" # Example"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" assert_eq!(12 + 1, 13);"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8294},{"Deduplicated":8295}],"output":{"Deduplicated":8348}},"item":{"id":124,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295},{"Deduplicated":8348}],"const_generics":[],"trait_refs":[{"HashConsedValue":[8376,{"kind":"SelfId","trait_decl_ref":{"regions":[],"skip_binder":{"id":14,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295},{"Deduplicated":8348}],"const_generics":[],"trait_refs":[]}}}}]}]}}},"kind":{"TraitMethod":[14,0]}}],"vtable":{"id":{"Adt":14},"generics":{"regions":[],"types":[{"Deduplicated":8295},{"Deduplicated":8348}],"const_generics":[],"trait_refs":[]}}},{"def_id":15,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["ops",0]},{"Ident":["arith",0]},{"Ident":["Mul",0]}],"span":{"data":{"file_id":14,"beg":{"line":322,"col":0},"end":{"line":322,"col":31}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" The multiplication operator `*`."},{"DocComment":""},{"DocComment":" Note that `Rhs` is `Self` by default, but this is not mandatory."},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" ## `Mul`tipliable rational numbers"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" use std::ops::Mul;"},{"DocComment":""},{"DocComment":" // By the fundamental theorem of arithmetic, rational numbers in lowest"},{"DocComment":" // terms are unique. So, by keeping `Rational`s in reduced form, we can"},{"DocComment":" // derive `Eq` and `PartialEq`."},{"DocComment":" #[derive(Debug, Eq, PartialEq)]"},{"DocComment":" struct Rational {"},{"DocComment":" numerator: usize,"},{"DocComment":" denominator: usize,"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl Rational {"},{"DocComment":" fn new(numerator: usize, denominator: usize) -> Self {"},{"DocComment":" if denominator == 0 {"},{"DocComment":" panic!(\"Zero is an invalid denominator!\");"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" // Reduce to lowest terms by dividing by the greatest common"},{"DocComment":" // divisor."},{"DocComment":" let gcd = gcd(numerator, denominator);"},{"DocComment":" Self {"},{"DocComment":" numerator: numerator / gcd,"},{"DocComment":" denominator: denominator / gcd,"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl Mul for Rational {"},{"DocComment":" // The multiplication of rational numbers is a closed operation."},{"DocComment":" type Output = Self;"},{"DocComment":""},{"DocComment":" fn mul(self, rhs: Self) -> Self {"},{"DocComment":" let numerator = self.numerator * rhs.numerator;"},{"DocComment":" let denominator = self.denominator * rhs.denominator;"},{"DocComment":" Self::new(numerator, denominator)"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" // Euclid's two-thousand-year-old algorithm for finding the greatest common"},{"DocComment":" // divisor."},{"DocComment":" fn gcd(x: usize, y: usize) -> usize {"},{"DocComment":" let mut x = x;"},{"DocComment":" let mut y = y;"},{"DocComment":" while y != 0 {"},{"DocComment":" let t = y;"},{"DocComment":" y = x % y;"},{"DocComment":" x = t;"},{"DocComment":" }"},{"DocComment":" x"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" assert_eq!(Rational::new(1, 2), Rational::new(2, 4));"},{"DocComment":" assert_eq!(Rational::new(2, 3) * Rational::new(3, 4),"},{"DocComment":" Rational::new(1, 2));"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" ## Multiplying vectors by scalars as in linear algebra"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" use std::ops::Mul;"},{"DocComment":""},{"DocComment":" struct Scalar { value: usize }"},{"DocComment":""},{"DocComment":" #[derive(Debug, PartialEq)]"},{"DocComment":" struct Vector { value: Vec<usize> }"},{"DocComment":""},{"DocComment":" impl Mul<Scalar> for Vector {"},{"DocComment":" type Output = Self;"},{"DocComment":""},{"DocComment":" fn mul(self, rhs: Scalar) -> Self::Output {"},{"DocComment":" Self { value: self.value.iter().map(|v| v * rhs.value).collect() }"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" let vector = Vector { value: vec![2, 4, 6] };"},{"DocComment":" let scalar = Scalar { value: 3 };"},{"DocComment":" assert_eq!(vector * scalar, Vector { value: vec![6, 12, 18] });"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"mul"},"generics":{"regions":[],"types":[{"index":0,"name":"Self"},{"index":1,"name":"Rhs"},{"index":2,"name":"Self_Output"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[],"consts":[],"types":[null],"methods":[{"params":{"regions":[],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"mul","attr_info":{"attributes":[{"DocComment":" Performs the `*` operation."},{"DocComment":""},{"DocComment":" # Example"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" assert_eq!(12 * 2, 24);"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8294},{"Deduplicated":8295}],"output":{"Deduplicated":8348}},"item":{"id":125,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295},{"Deduplicated":8348}],"const_generics":[],"trait_refs":[{"HashConsedValue":[8377,{"kind":"SelfId","trait_decl_ref":{"regions":[],"skip_binder":{"id":15,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295},{"Deduplicated":8348}],"const_generics":[],"trait_refs":[]}}}}]}]}}},"kind":{"TraitMethod":[15,0]}}],"vtable":{"id":{"Adt":15},"generics":{"regions":[],"types":[{"Deduplicated":8295},{"Deduplicated":8348}],"const_generics":[],"trait_refs":[]}}},{"def_id":16,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["ops",0]},{"Ident":["arith",0]},{"Ident":["SubAssign",0]}],"span":{"data":{"file_id":14,"beg":{"line":839,"col":0},"end":{"line":839,"col":37}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" The subtraction assignment operator `-=`."},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" This example creates a `Point` struct that implements the `SubAssign`"},{"DocComment":" trait, and then demonstrates sub-assigning to a mutable `Point`."},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" use std::ops::SubAssign;"},{"DocComment":""},{"DocComment":" #[derive(Debug, Copy, Clone, PartialEq)]"},{"DocComment":" struct Point {"},{"DocComment":" x: i32,"},{"DocComment":" y: i32,"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl SubAssign for Point {"},{"DocComment":" fn sub_assign(&mut self, other: Self) {"},{"DocComment":" *self = Self {"},{"DocComment":" x: self.x - other.x,"},{"DocComment":" y: self.y - other.y,"},{"DocComment":" };"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" let mut point = Point { x: 3, y: 3 };"},{"DocComment":" point -= Point { x: 2, y: 3 };"},{"DocComment":" assert_eq!(point, Point {x: 1, y: 0});"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"sub_assign"},"generics":{"regions":[],"types":[{"index":0,"name":"Self"},{"index":1,"name":"Rhs"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[],"consts":[],"types":[],"methods":[{"params":{"regions":[{"index":0,"name":null,"mutability":"Unknown"}],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"sub_assign","attr_info":{"attributes":[{"DocComment":" Performs the `-=` operation."},{"DocComment":""},{"DocComment":" # Example"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" let mut x: u32 = 12;"},{"DocComment":" x -= 1;"},{"DocComment":" assert_eq!(x, 11);"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8363},{"Deduplicated":8295}],"output":{"Deduplicated":1108}},"item":{"id":126,"generics":{"regions":[{"Var":{"Bound":[0,0]}}],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[{"HashConsedValue":[8378,{"kind":"SelfId","trait_decl_ref":{"regions":[],"skip_binder":{"id":16,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}}}]}]}}},"kind":{"TraitMethod":[16,0]}}],"vtable":{"id":{"Adt":16},"generics":{"regions":[],"types":[{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}},{"def_id":17,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["ops",0]},{"Ident":["arith",0]},{"Ident":["AddAssign",0]}],"span":{"data":{"file_id":14,"beg":{"line":768,"col":0},"end":{"line":768,"col":37}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" The addition assignment operator `+=`."},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" This example creates a `Point` struct that implements the `AddAssign`"},{"DocComment":" trait, and then demonstrates add-assigning to a mutable `Point`."},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" use std::ops::AddAssign;"},{"DocComment":""},{"DocComment":" #[derive(Debug, Copy, Clone, PartialEq)]"},{"DocComment":" struct Point {"},{"DocComment":" x: i32,"},{"DocComment":" y: i32,"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl AddAssign for Point {"},{"DocComment":" fn add_assign(&mut self, other: Self) {"},{"DocComment":" *self = Self {"},{"DocComment":" x: self.x + other.x,"},{"DocComment":" y: self.y + other.y,"},{"DocComment":" };"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" let mut point = Point { x: 1, y: 0 };"},{"DocComment":" point += Point { x: 2, y: 3 };"},{"DocComment":" assert_eq!(point, Point { x: 3, y: 3 });"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"add_assign"},"generics":{"regions":[],"types":[{"index":0,"name":"Self"},{"index":1,"name":"Rhs"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[],"consts":[],"types":[],"methods":[{"params":{"regions":[{"index":0,"name":null,"mutability":"Unknown"}],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"add_assign","attr_info":{"attributes":[{"DocComment":" Performs the `+=` operation."},{"DocComment":""},{"DocComment":" # Example"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" let mut x: u32 = 12;"},{"DocComment":" x += 1;"},{"DocComment":" assert_eq!(x, 13);"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8363},{"Deduplicated":8295}],"output":{"Deduplicated":1108}},"item":{"id":127,"generics":{"regions":[{"Var":{"Bound":[0,0]}}],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[{"HashConsedValue":[8379,{"kind":"SelfId","trait_decl_ref":{"regions":[],"skip_binder":{"id":17,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}}}]}]}}},"kind":{"TraitMethod":[17,0]}}],"vtable":{"id":{"Adt":17},"generics":{"regions":[],"types":[{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}},{"def_id":18,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["ops",0]},{"Ident":["arith",0]},{"Ident":["MulAssign",0]}],"span":{"data":{"file_id":14,"beg":{"line":901,"col":0},"end":{"line":901,"col":37}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" The multiplication assignment operator `*=`."},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" use std::ops::MulAssign;"},{"DocComment":""},{"DocComment":" #[derive(Debug, PartialEq)]"},{"DocComment":" struct Frequency { hertz: f64 }"},{"DocComment":""},{"DocComment":" impl MulAssign<f64> for Frequency {"},{"DocComment":" fn mul_assign(&mut self, rhs: f64) {"},{"DocComment":" self.hertz *= rhs;"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" let mut frequency = Frequency { hertz: 50.0 };"},{"DocComment":" frequency *= 4.0;"},{"DocComment":" assert_eq!(Frequency { hertz: 200.0 }, frequency);"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"mul_assign"},"generics":{"regions":[],"types":[{"index":0,"name":"Self"},{"index":1,"name":"Rhs"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[],"consts":[],"types":[],"methods":[{"params":{"regions":[{"index":0,"name":null,"mutability":"Unknown"}],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"mul_assign","attr_info":{"attributes":[{"DocComment":" Performs the `*=` operation."},{"DocComment":""},{"DocComment":" # Example"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" let mut x: u32 = 12;"},{"DocComment":" x *= 2;"},{"DocComment":" assert_eq!(x, 24);"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8363},{"Deduplicated":8295}],"output":{"Deduplicated":1108}},"item":{"id":128,"generics":{"regions":[{"Var":{"Bound":[0,0]}}],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[{"HashConsedValue":[8380,{"kind":"SelfId","trait_decl_ref":{"regions":[],"skip_binder":{"id":18,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}}}]}]}}},"kind":{"TraitMethod":[18,0]}}],"vtable":{"id":{"Adt":18},"generics":{"regions":[],"types":[{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}},{"def_id":19,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["borrow",0]},{"Ident":["Borrow",0]}],"span":{"data":{"file_id":15,"beg":{"line":158,"col":0},"end":{"line":158,"col":40}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" A trait for borrowing data."},{"DocComment":""},{"DocComment":" In Rust, it is common to provide different representations of a type for"},{"DocComment":" different use cases. For instance, storage location and management for a"},{"DocComment":" value can be specifically chosen as appropriate for a particular use via"},{"DocComment":" pointer types such as [`Box<T>`] or [`Rc<T>`]. Beyond these generic"},{"DocComment":" wrappers that can be used with any type, some types provide optional"},{"DocComment":" facets providing potentially costly functionality. An example for such a"},{"DocComment":" type is [`String`] which adds the ability to extend a string to the basic"},{"DocComment":" [`str`]. This requires keeping additional information unnecessary for a"},{"DocComment":" simple, immutable string."},{"DocComment":""},{"DocComment":" These types provide access to the underlying data through references"},{"DocComment":" to the type of that data. They are said to be ‘borrowed as’ that type."},{"DocComment":" For instance, a [`Box<T>`] can be borrowed as `T` while a [`String`]"},{"DocComment":" can be borrowed as `str`."},{"DocComment":""},{"DocComment":" Types express that they can be borrowed as some type `T` by implementing"},{"DocComment":" `Borrow<T>`, providing a reference to a `T` in the trait’s"},{"DocComment":" [`borrow`] method. A type is free to borrow as several different types."},{"DocComment":" If it wishes to mutably borrow as the type, allowing the underlying data"},{"DocComment":" to be modified, it can additionally implement [`BorrowMut<T>`]."},{"DocComment":""},{"DocComment":" Further, when providing implementations for additional traits, it needs"},{"DocComment":" to be considered whether they should behave identically to those of the"},{"DocComment":" underlying type as a consequence of acting as a representation of that"},{"DocComment":" underlying type. Generic code typically uses `Borrow<T>` when it relies"},{"DocComment":" on the identical behavior of these additional trait implementations."},{"DocComment":" These traits will likely appear as additional trait bounds."},{"DocComment":""},{"DocComment":" In particular `Eq`, `Ord` and `Hash` must be equivalent for"},{"DocComment":" borrowed and owned values: `x.borrow() == y.borrow()` should give the"},{"DocComment":" same result as `x == y`."},{"DocComment":""},{"DocComment":" If generic code merely needs to work for all types that can"},{"DocComment":" provide a reference to related type `T`, it is often better to use"},{"DocComment":" [`AsRef<T>`] as more types can safely implement it."},{"DocComment":""},{"DocComment":" [`Box<T>`]: ../../std/boxed/struct.Box.html"},{"DocComment":" [`Mutex<T>`]: ../../std/sync/struct.Mutex.html"},{"DocComment":" [`Rc<T>`]: ../../std/rc/struct.Rc.html"},{"DocComment":" [`String`]: ../../std/string/struct.String.html"},{"DocComment":" [`borrow`]: Borrow::borrow"},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" As a data collection, [`HashMap<K, V>`] owns both keys and values. If"},{"DocComment":" the key’s actual data is wrapped in a managing type of some kind, it"},{"DocComment":" should, however, still be possible to search for a value using a"},{"DocComment":" reference to the key’s data. For instance, if the key is a string, then"},{"DocComment":" it is likely stored with the hash map as a [`String`], while it should"},{"DocComment":" be possible to search using a [`&str`][`str`]. Thus, `insert` needs to"},{"DocComment":" operate on a `String` while `get` needs to be able to use a `&str`."},{"DocComment":""},{"DocComment":" Slightly simplified, the relevant parts of `HashMap<K, V>` look like"},{"DocComment":" this:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" use std::borrow::Borrow;"},{"DocComment":" use std::hash::Hash;"},{"DocComment":""},{"DocComment":" pub struct HashMap<K, V> {"},{"DocComment":" # marker: ::std::marker::PhantomData<(K, V)>,"},{"DocComment":" // fields omitted"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl<K, V> HashMap<K, V> {"},{"DocComment":" pub fn insert(&self, key: K, value: V) -> Option<V>"},{"DocComment":" where K: Hash + Eq"},{"DocComment":" {"},{"DocComment":" # unimplemented!()"},{"DocComment":" // ..."},{"DocComment":" }"},{"DocComment":""},{"DocComment":" pub fn get<Q>(&self, k: &Q) -> Option<&V>"},{"DocComment":" where"},{"DocComment":" K: Borrow<Q>,"},{"DocComment":" Q: Hash + Eq + ?Sized"},{"DocComment":" {"},{"DocComment":" # unimplemented!()"},{"DocComment":" // ..."},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" The entire hash map is generic over a key type `K`. Because these keys"},{"DocComment":" are stored with the hash map, this type has to own the key’s data."},{"DocComment":" When inserting a key-value pair, the map is given such a `K` and needs"},{"DocComment":" to find the correct hash bucket and check if the key is already present"},{"DocComment":" based on that `K`. It therefore requires `K: Hash + Eq`."},{"DocComment":""},{"DocComment":" When searching for a value in the map, however, having to provide a"},{"DocComment":" reference to a `K` as the key to search for would require to always"},{"DocComment":" create such an owned value. For string keys, this would mean a `String`"},{"DocComment":" value needs to be created just for the search for cases where only a"},{"DocComment":" `str` is available."},{"DocComment":""},{"DocComment":" Instead, the `get` method is generic over the type of the underlying key"},{"DocComment":" data, called `Q` in the method signature above. It states that `K`"},{"DocComment":" borrows as a `Q` by requiring that `K: Borrow<Q>`. By additionally"},{"DocComment":" requiring `Q: Hash + Eq`, it signals the requirement that `K` and `Q`"},{"DocComment":" have implementations of the `Hash` and `Eq` traits that produce identical"},{"DocComment":" results."},{"DocComment":""},{"DocComment":" The implementation of `get` relies in particular on identical"},{"DocComment":" implementations of `Hash` by determining the key’s hash bucket by calling"},{"DocComment":" `Hash::hash` on the `Q` value even though it inserted the key based on"},{"DocComment":" the hash value calculated from the `K` value."},{"DocComment":""},{"DocComment":" As a consequence, the hash map breaks if a `K` wrapping a `Q` value"},{"DocComment":" produces a different hash than `Q`. For instance, imagine you have a"},{"DocComment":" type that wraps a string but compares ASCII letters ignoring their case:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" pub struct CaseInsensitiveString(String);"},{"DocComment":""},{"DocComment":" impl PartialEq for CaseInsensitiveString {"},{"DocComment":" fn eq(&self, other: &Self) -> bool {"},{"DocComment":" self.0.eq_ignore_ascii_case(&other.0)"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl Eq for CaseInsensitiveString { }"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" Because two equal values need to produce the same hash value, the"},{"DocComment":" implementation of `Hash` needs to ignore ASCII case, too:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" # use std::hash::{Hash, Hasher};"},{"DocComment":" # pub struct CaseInsensitiveString(String);"},{"DocComment":" impl Hash for CaseInsensitiveString {"},{"DocComment":" fn hash<H: Hasher>(&self, state: &mut H) {"},{"DocComment":" for c in self.0.as_bytes() {"},{"DocComment":" c.to_ascii_lowercase().hash(state)"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" Can `CaseInsensitiveString` implement `Borrow<str>`? It certainly can"},{"DocComment":" provide a reference to a string slice via its contained owned string."},{"DocComment":" But because its `Hash` implementation differs, it behaves differently"},{"DocComment":" from `str` and therefore must not, in fact, implement `Borrow<str>`."},{"DocComment":" If it wants to allow others access to the underlying `str`, it can do"},{"DocComment":" that via `AsRef<str>` which doesn’t carry any extra requirements."},{"DocComment":""},{"DocComment":" [`Hash`]: crate::hash::Hash"},{"DocComment":" [`HashMap<K, V>`]: ../../std/collections/struct.HashMap.html"},{"DocComment":" [`String`]: ../../std/string/struct.String.html"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"Borrow"},"generics":{"regions":[],"types":[{"index":0,"name":"Self"},{"index":1,"name":"Borrowed"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[],"consts":[],"types":[],"methods":[{"params":{"regions":[{"index":0,"name":null,"mutability":"Unknown"}],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"borrow","attr_info":{"attributes":[{"DocComment":" Immutably borrows from an owned value."},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" use std::borrow::Borrow;"},{"DocComment":""},{"DocComment":" fn check<T: Borrow<str>>(s: T) {"},{"DocComment":" assert_eq!(\"Hello\", s.borrow());"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" let s = \"Hello\".to_string();"},{"DocComment":""},{"DocComment":" check(s);"},{"DocComment":""},{"DocComment":" let s = \"Hello\";"},{"DocComment":""},{"DocComment":" check(s);"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8361}],"output":{"HashConsedValue":[8381,{"Ref":[{"Var":{"Bound":[0,0]}},{"Deduplicated":8295},"Shared"]}]}},"item":{"id":129,"generics":{"regions":[{"Var":{"Bound":[0,0]}}],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[{"HashConsedValue":[8382,{"kind":"SelfId","trait_decl_ref":{"regions":[],"skip_binder":{"id":19,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}}}]}]}}},"kind":{"TraitMethod":[19,0]}}],"vtable":{"id":{"Adt":19},"generics":{"regions":[],"types":[{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}},{"def_id":20,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["iter",0]},{"Ident":["traits",0]},{"Ident":["accum",0]},{"Ident":["Sum",0]}],"span":{"data":{"file_id":16,"beg":{"line":18,"col":0},"end":{"line":18,"col":36}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" Trait to represent types that can be created by summing up an iterator."},{"DocComment":""},{"DocComment":" This trait is used to implement [`Iterator::sum()`]. Types which implement"},{"DocComment":" this trait can be generated by using the [`sum()`] method on an iterator."},{"DocComment":" Like [`FromIterator`], this trait should rarely be called directly."},{"DocComment":""},{"DocComment":" [`sum()`]: Iterator::sum"},{"DocComment":" [`FromIterator`]: iter::FromIterator"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":null},"generics":{"regions":[],"types":[{"index":0,"name":"Self"},{"index":1,"name":"A"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[],"consts":[],"types":[],"methods":[{"params":{"regions":[],"types":[{"index":0,"name":"I"}],"const_generics":[],"trait_clauses":[{"clause_id":0,"span":{"data":{"file_id":16,"beg":{"line":22,"col":14},"end":{"line":22,"col":32}},"generated_from_span":null},"origin":"WhereClauseOnFn","trait_":{"regions":[],"skip_binder":{"id":21,"generics":{"regions":[],"types":[{"HashConsedValue":[1092,{"TypeVar":{"Bound":[1,0]}}]},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}}}],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"sum","attr_info":{"attributes":[{"DocComment":" Takes an iterator and generates `Self` from the elements by \"summing up\""},{"DocComment":" the items."}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":1091}],"output":{"Deduplicated":8294}},"item":{"id":130,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295},{"Deduplicated":1091}],"const_generics":[],"trait_refs":[{"HashConsedValue":[8383,{"kind":"SelfId","trait_decl_ref":{"regions":[],"skip_binder":{"id":20,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}}}]},{"HashConsedValue":[8384,{"kind":{"Clause":{"Bound":[0,0]}},"trait_decl_ref":{"regions":[],"skip_binder":{"id":21,"generics":{"regions":[],"types":[{"Deduplicated":1092},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}}}]}]}}},"kind":{"TraitMethod":[20,0]}}],"vtable":null},{"def_id":21,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["iter",0]},{"Ident":["traits",0]},{"Ident":["iterator",0]},{"Ident":["Iterator",0]}],"span":{"data":{"file_id":19,"beg":{"line":42,"col":0},"end":{"line":42,"col":24}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" A trait for dealing with iterators."},{"DocComment":""},{"DocComment":" This is the main iterator trait. For more about the concept of iterators"},{"DocComment":" generally, please see the [module-level documentation]. In particular, you"},{"DocComment":" may want to know how to [implement `Iterator`][impl]."},{"DocComment":""},{"DocComment":" [module-level documentation]: crate::iter"},{"DocComment":" [impl]: crate::iter#implementing-iterator"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"iterator"},"generics":{"regions":[],"types":[{"index":0,"name":"Self"},{"index":1,"name":"Self_Item"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[],"consts":[],"types":[null],"methods":[{"params":{"regions":[{"index":0,"name":null,"mutability":"Unknown"}],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"next","attr_info":{"attributes":[{"DocComment":" Advances the iterator and returns the next value."},{"DocComment":""},{"DocComment":" Returns [`None`] when iteration is finished. Individual iterator"},{"DocComment":" implementations may choose to resume iteration, and so calling `next()`"},{"DocComment":" again may or may not eventually start returning [`Some(Item)`] again at some"},{"DocComment":" point."},{"DocComment":""},{"DocComment":" [`Some(Item)`]: Some"},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" let a = [1, 2, 3];"},{"DocComment":""},{"DocComment":" let mut iter = a.into_iter();"},{"DocComment":""},{"DocComment":" // A call to next() returns the next value..."},{"DocComment":" assert_eq!(Some(1), iter.next());"},{"DocComment":" assert_eq!(Some(2), iter.next());"},{"DocComment":" assert_eq!(Some(3), iter.next());"},{"DocComment":""},{"DocComment":" // ... and then None once it's over."},{"DocComment":" assert_eq!(None, iter.next());"},{"DocComment":""},{"DocComment":" // More calls may or may not return `None`. Here, they always will."},{"DocComment":" assert_eq!(None, iter.next());"},{"DocComment":" assert_eq!(None, iter.next());"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8363}],"output":{"Deduplicated":8385}},"item":{"id":131,"generics":{"regions":[{"Var":{"Bound":[0,0]}}],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[{"HashConsedValue":[8386,{"kind":"SelfId","trait_decl_ref":{"regions":[],"skip_binder":{"id":21,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}}}]}]}}},"kind":{"TraitMethod":[21,0]}},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"vtable":{"id":{"Adt":20},"generics":{"regions":[],"types":[{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}},{"def_id":22,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["iter",0]},{"Ident":["traits",0]},{"Ident":["accum",0]},{"Ident":["Product",0]}],"span":{"data":{"file_id":16,"beg":{"line":40,"col":0},"end":{"line":40,"col":40}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" Trait to represent types that can be created by multiplying elements of an"},{"DocComment":" iterator."},{"DocComment":""},{"DocComment":" This trait is used to implement [`Iterator::product()`]. 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Rust implements `Default` for various primitive types."},{"DocComment":""},{"DocComment":" If you want to override a particular option, but still retain the other defaults:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" # #[allow(dead_code)]"},{"DocComment":" # #[derive(Default)]"},{"DocComment":" # struct SomeOptions {"},{"DocComment":" # foo: i32,"},{"DocComment":" # bar: f32,"},{"DocComment":" # }"},{"DocComment":" fn main() {"},{"DocComment":" let options = SomeOptions { foo: 42, ..Default::default() };"},{"DocComment":" }"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" ## Derivable"},{"DocComment":""},{"DocComment":" This trait can be used with `#[derive]` if all of the type's fields implement"},{"DocComment":" `Default`. When `derive`d, it will use the default value for each field's type."},{"DocComment":""},{"DocComment":" ### `enum`s"},{"DocComment":""},{"DocComment":" When using `#[derive(Default)]` on an `enum`, you need to choose which unit variant will be"},{"DocComment":" default. You do this by placing the `#[default]` attribute on the variant."},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" #[derive(Default)]"},{"DocComment":" enum Kind {"},{"DocComment":" #[default]"},{"DocComment":" A,"},{"DocComment":" B,"},{"DocComment":" C,"},{"DocComment":" }"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" You cannot use the `#[default]` attribute on non-unit or non-exhaustive variants."},{"DocComment":""},{"DocComment":" The `#[default]` attribute was stabilized in Rust 1.62.0."},{"DocComment":""},{"DocComment":" ## How can I implement `Default`?"},{"DocComment":""},{"DocComment":" Provide an implementation for the `default()` method that returns the value of"},{"DocComment":" your type that should be the default:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" # #![allow(dead_code)]"},{"DocComment":" enum Kind {"},{"DocComment":" A,"},{"DocComment":" B,"},{"DocComment":" C,"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl 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zero;"},{"DocComment":" - $(\\textsf{false}, 0)$, if $\\textsf{num}$ is nonzero and $\\textsf{div}$ is zero;"},{"DocComment":" - $(\\textsf{false}, \\sqrt{G_S \\cdot \\textsf{num}/\\textsf{div}})$, if"},{"DocComment":" $\\textsf{num}$ and $\\textsf{div}$ are nonzero and $\\textsf{num}/\\textsf{div}$ is"},{"DocComment":" a nonsquare in the field;"},{"DocComment":""},{"DocComment":" where $G_S$ is a non-square."},{"DocComment":""},{"DocComment":" # Warnings"},{"DocComment":""},{"DocComment":" - The choice of root from `sqrt` is unspecified."},{"DocComment":" - The value of $G_S$ is unspecified, and cannot be assumed to have any specific"},{"DocComment":" value in a generic context."}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8361},{"Deduplicated":8369}],"output":{"Deduplicated":8391}},"item":{"id":90,"generics":{"regions":[{"Var":{"Bound":[0,0]}},{"Var":{"Bound":[0,1]}}],"types":[{"Deduplicated":8294}],"const_generics":[],"trait_refs":[{"Deduplicated":8389}]}}},"kind":{"TraitMethod":[24,7]}},null,{"params":{"regions":[{"index":0,"name":null,"mutability":"Unknown"}],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"sqrt","attr_info":{"attributes":[{"DocComment":" Returns the square root of the field element, if it is"},{"DocComment":" quadratic residue."},{"DocComment":""},{"DocComment":" The provided method is implemented in terms of [`Self::sqrt_ratio`]."}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8361}],"output":{"Deduplicated":8390}},"item":{"id":92,"generics":{"regions":[{"Var":{"Bound":[0,0]}}],"types":[{"Deduplicated":8294}],"const_generics":[],"trait_refs":[{"Deduplicated":8389}]}}},"kind":{"TraitMethod":[24,9]}},null,{"params":{"regions":[{"index":0,"name":null,"mutability":"Unknown"}],"types":[{"index":0,"name":"S"}],"const_generics":[],"trait_clauses":[{"clause_id":0,"span":{"data":{"file_id":21,"beg":{"line":178,"col":22},"end":{"line":178,"col":34}},"generated_from_span":null},"origin":"WhereClauseOnFn","trait_":{"regions":[],"skip_binder":{"id":28,"generics":{"regions":[],"types":[{"Deduplicated":1092},{"Deduplicated":2074}],"const_generics":[],"trait_refs":[]}}}}],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"pow_vartime","attr_info":{"attributes":[{"DocComment":" Exponentiates `self` by `exp`, where `exp` is a little-endian order integer"},{"DocComment":" exponent."},{"DocComment":""},{"DocComment":" # Guarantees"},{"DocComment":""},{"DocComment":" **This operation is variable time with respect to `self`, for all exponent.** If"},{"DocComment":" the exponent is fixed, this operation is effectively constant time. However, for"},{"DocComment":" stronger constant-time guarantees, [`Field::pow`] should be used."}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8361},{"Deduplicated":1091}],"output":{"Deduplicated":8294}},"item":{"id":94,"generics":{"regions":[{"Var":{"Bound":[0,0]}}],"types":[{"Deduplicated":8294},{"Deduplicated":1091}],"const_generics":[],"trait_refs":[{"Deduplicated":8389},{"HashConsedValue":[2077,{"kind":{"Clause":{"Bound":[0,0]}},"trait_decl_ref":{"regions":[],"skip_binder":{"id":28,"generics":{"regions":[],"types":[{"Deduplicated":1092},{"Deduplicated":2074}],"const_generics":[],"trait_refs":[]}}}}]}]}}},"kind":{"TraitMethod":[24,11]}}],"vtable":null},{"def_id":25,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["marker",0]},{"Ident":["Send",0]}],"span":{"data":{"file_id":6,"beg":{"line":92,"col":0},"end":{"line":92,"col":26}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" Types that can be transferred across thread boundaries."},{"DocComment":""},{"DocComment":" This trait is automatically implemented when the compiler determines it's"},{"DocComment":" appropriate."},{"DocComment":""},{"DocComment":" An example of a non-`Send` type is the reference-counting pointer"},{"DocComment":" [`rc::Rc`][`Rc`]. If two threads attempt to clone [`Rc`]s that point to the same"},{"DocComment":" reference-counted value, they might try to update the reference count at the"},{"DocComment":" same time, which is [undefined behavior][ub] because [`Rc`] doesn't use atomic"},{"DocComment":" operations. Its cousin [`sync::Arc`][arc] does use atomic operations (incurring"},{"DocComment":" some overhead) and thus is `Send`."},{"DocComment":""},{"DocComment":" See [the Nomicon](../../nomicon/send-and-sync.html) and the [`Sync`] trait for more details."},{"DocComment":""},{"DocComment":" [`Rc`]: ../../std/rc/struct.Rc.html"},{"DocComment":" [arc]: ../../std/sync/struct.Arc.html"},{"DocComment":" [ub]: ../../reference/behavior-considered-undefined.html"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"Send"},"generics":{"regions":[],"types":[{"index":0,"name":"Self"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[],"consts":[],"types":[],"methods":[],"vtable":{"id":{"Adt":49},"generics":{"regions":[],"types":[],"const_generics":[],"trait_refs":[]}}},{"def_id":26,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["marker",0]},{"Ident":["Sync",0]}],"span":{"data":{"file_id":6,"beg":{"line":657,"col":0},"end":{"line":657,"col":26}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" Types for which it is safe to share references between threads."},{"DocComment":""},{"DocComment":" This trait is automatically implemented when the compiler determines"},{"DocComment":" it's appropriate."},{"DocComment":""},{"DocComment":" The precise definition is: a type `T` is [`Sync`] if and only if `&T` is"},{"DocComment":" [`Send`]. In other words, if there is no possibility of"},{"DocComment":" [undefined behavior][ub] (including data races) when passing"},{"DocComment":" `&T` references between threads."},{"DocComment":""},{"DocComment":" As one would expect, primitive types like [`u8`] and [`f64`]"},{"DocComment":" are all [`Sync`], and so are simple aggregate types containing them,"},{"DocComment":" like tuples, structs and enums. More examples of basic [`Sync`]"},{"DocComment":" types include \"immutable\" types like `&T`, and those with simple"},{"DocComment":" inherited mutability, such as [`Box<T>`][box], [`Vec<T>`][vec] and"},{"DocComment":" most other collection types. (Generic parameters need to be [`Sync`]"},{"DocComment":" for their container to be [`Sync`].)"},{"DocComment":""},{"DocComment":" A somewhat surprising consequence of the definition is that `&mut T`"},{"DocComment":" is `Sync` (if `T` is `Sync`) even though it seems like that might"},{"DocComment":" provide unsynchronized mutation. The trick is that a mutable"},{"DocComment":" reference behind a shared reference (that is, `& &mut T`)"},{"DocComment":" becomes read-only, as if it were a `& &T`. Hence there is no risk"},{"DocComment":" of a data race."},{"DocComment":""},{"DocComment":" A shorter overview of how [`Sync`] and [`Send`] relate to referencing:"},{"DocComment":" * `&T` is [`Send`] if and only if `T` is [`Sync`]"},{"DocComment":" * `&mut T` is [`Send`] if and only if `T` is [`Send`]"},{"DocComment":" * `&T` and `&mut T` are [`Sync`] if and only if `T` is [`Sync`]"},{"DocComment":""},{"DocComment":" Types that are not `Sync` are those that have \"interior"},{"DocComment":" mutability\" in a non-thread-safe form, such as [`Cell`][cell]"},{"DocComment":" and [`RefCell`][refcell]. These types allow for mutation of"},{"DocComment":" their contents even through an immutable, shared reference. For"},{"DocComment":" example the `set` method on [`Cell<T>`][cell] takes `&self`, so it requires"},{"DocComment":" only a shared reference [`&Cell<T>`][cell]. The method performs no"},{"DocComment":" synchronization, thus [`Cell`][cell] cannot be `Sync`."},{"DocComment":""},{"DocComment":" Another example of a non-`Sync` type is the reference-counting"},{"DocComment":" pointer [`Rc`][rc]. Given any reference [`&Rc<T>`][rc], you can clone"},{"DocComment":" a new [`Rc<T>`][rc], modifying the reference counts in a non-atomic way."},{"DocComment":""},{"DocComment":" For cases when one does need thread-safe interior mutability,"},{"DocComment":" Rust provides [atomic data types], as well as explicit locking via"},{"DocComment":" [`sync::Mutex`][mutex] and [`sync::RwLock`][rwlock]. These types"},{"DocComment":" ensure that any mutation cannot cause data races, hence the types"},{"DocComment":" are `Sync`. Likewise, [`sync::Arc`][arc] provides a thread-safe"},{"DocComment":" analogue of [`Rc`][rc]."},{"DocComment":""},{"DocComment":" Any types with interior mutability must also use the"},{"DocComment":" [`cell::UnsafeCell`][unsafecell] wrapper around the value(s) which"},{"DocComment":" can be mutated through a shared reference. Failing to doing this is"},{"DocComment":" [undefined behavior][ub]. For example, [`transmute`][transmute]-ing"},{"DocComment":" from `&T` to `&mut T` is invalid."},{"DocComment":""},{"DocComment":" See [the Nomicon][nomicon-send-and-sync] for more details about `Sync`."},{"DocComment":""},{"DocComment":" [box]: ../../std/boxed/struct.Box.html"},{"DocComment":" [vec]: ../../std/vec/struct.Vec.html"},{"DocComment":" [cell]: crate::cell::Cell"},{"DocComment":" [refcell]: crate::cell::RefCell"},{"DocComment":" [rc]: ../../std/rc/struct.Rc.html"},{"DocComment":" [arc]: ../../std/sync/struct.Arc.html"},{"DocComment":" [atomic data types]: crate::sync::atomic"},{"DocComment":" [mutex]: ../../std/sync/struct.Mutex.html"},{"DocComment":" [rwlock]: ../../std/sync/struct.RwLock.html"},{"DocComment":" [unsafecell]: crate::cell::UnsafeCell"},{"DocComment":" [ub]: ../../reference/behavior-considered-undefined.html"},{"DocComment":" [transmute]: crate::mem::transmute"},{"DocComment":" [nomicon-send-and-sync]: ../../nomicon/send-and-sync.html"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"sync"},"generics":{"regions":[],"types":[{"index":0,"name":"Self"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[],"consts":[],"types":[],"methods":[],"vtable":{"id":{"Adt":50},"generics":{"regions":[],"types":[],"const_generics":[],"trait_refs":[]}}},{"def_id":27,"item_meta":{"name":[{"Ident":["rand_core",0]},{"Ident":["RngCore",0]}],"span":{"data":{"file_id":22,"beg":{"line":142,"col":0},"end":{"line":142,"col":17}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" The core of a random number generator."},{"DocComment":""},{"DocComment":" This trait encapsulates the low-level functionality common to all"},{"DocComment":" generators, and is the \"back end\", to be implemented by generators."},{"DocComment":" End users should normally use the `Rng` trait from the [`rand`] crate,"},{"DocComment":" which is automatically implemented for every type implementing `RngCore`."},{"DocComment":""},{"DocComment":" Three different methods for generating random data are provided since the"},{"DocComment":" optimal implementation of each is dependent on the type of generator. There"},{"DocComment":" is no required relationship between the output of each; e.g. many"},{"DocComment":" implementations of [`fill_bytes`] consume a whole number of `u32` or `u64`"},{"DocComment":" values and drop any remaining unused bytes. The same can happen with the"},{"DocComment":" [`next_u32`] and [`next_u64`] methods, implementations may discard some"},{"DocComment":" random bits for efficiency."},{"DocComment":""},{"DocComment":" The [`try_fill_bytes`] method is a variant of [`fill_bytes`] allowing error"},{"DocComment":" handling; it is not deemed sufficiently useful to add equivalents for"},{"DocComment":" [`next_u32`] or [`next_u64`] since the latter methods are almost always used"},{"DocComment":" with algorithmic generators (PRNGs), which are normally infallible."},{"DocComment":""},{"DocComment":" Implementers should produce bits uniformly. Pathological RNGs (e.g. always"},{"DocComment":" returning the same value, or never setting certain bits) can break rejection"},{"DocComment":" sampling used by random distributions, and also break other RNGs when"},{"DocComment":" seeding them via [`SeedableRng::from_rng`]."},{"DocComment":""},{"DocComment":" Algorithmic generators implementing [`SeedableRng`] should normally have"},{"DocComment":" *portable, reproducible* output, i.e. fix Endianness when converting values"},{"DocComment":" to avoid platform differences, and avoid making any changes which affect"},{"DocComment":" output (except by communicating that the release has breaking changes)."},{"DocComment":""},{"DocComment":" Typically an RNG will implement only one of the methods available"},{"DocComment":" in this trait directly, then use the helper functions from the"},{"DocComment":" [`impls`] module to implement the other methods."},{"DocComment":""},{"DocComment":" It is recommended that implementations also implement:"},{"DocComment":""},{"DocComment":" - `Debug` with a custom implementation which *does not* print any internal"},{"DocComment":" state (at least, [`CryptoRng`]s should not risk leaking state through"},{"DocComment":" `Debug`)."},{"DocComment":" - `Serialize` and `Deserialize` (from Serde), preferably making Serde"},{"DocComment":" support optional at the crate level in PRNG libs."},{"DocComment":" - `Clone`, if possible."},{"DocComment":" - *never* implement `Copy` (accidental copies may cause repeated values)."},{"DocComment":" - *do not* implement `Default` for pseudorandom generators, but instead"},{"DocComment":" implement [`SeedableRng`], to guide users towards proper seeding."},{"DocComment":" External / hardware RNGs can choose to implement `Default`."},{"DocComment":" - `Eq` and `PartialEq` could be implemented, but are probably not useful."},{"DocComment":""},{"DocComment":" # Example"},{"DocComment":""},{"DocComment":" A simple example, obviously not generating very *random* output:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" #![allow(dead_code)]"},{"DocComment":" use rand_core::{RngCore, Error, impls};"},{"DocComment":""},{"DocComment":" struct CountingRng(u64);"},{"DocComment":""},{"DocComment":" impl RngCore for CountingRng {"},{"DocComment":" fn next_u32(&mut self) -> u32 {"},{"DocComment":" self.next_u64() as u32"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" fn next_u64(&mut self) -> u64 {"},{"DocComment":" self.0 += 1;"},{"DocComment":" self.0"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" fn fill_bytes(&mut self, dest: &mut [u8]) {"},{"DocComment":" impls::fill_bytes_via_next(self, dest)"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" fn try_fill_bytes(&mut self, dest: &mut [u8]) -> Result<(), Error> {"},{"DocComment":" Ok(self.fill_bytes(dest))"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" [`rand`]: https://docs.rs/rand"},{"DocComment":" [`try_fill_bytes`]: RngCore::try_fill_bytes"},{"DocComment":" [`fill_bytes`]: RngCore::fill_bytes"},{"DocComment":" [`next_u32`]: RngCore::next_u32"},{"DocComment":" [`next_u64`]: RngCore::next_u64"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":null},"generics":{"regions":[],"types":[{"index":0,"name":"Self"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[],"consts":[],"types":[],"methods":[{"params":{"regions":[{"index":0,"name":null,"mutability":"Unknown"}],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"next_u32","attr_info":{"attributes":[{"DocComment":" Return the next random `u32`."},{"DocComment":""},{"DocComment":" RNGs must implement at least one method from this trait directly. In"},{"DocComment":" the case this method is not implemented directly, it can be implemented"},{"DocComment":" using `self.next_u64() as u32` or via [`impls::next_u32_via_fill`]."}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8363}],"output":{"Deduplicated":1834}},"item":{"id":219,"generics":{"regions":[{"Var":{"Bound":[0,0]}}],"types":[{"Deduplicated":8294}],"const_generics":[],"trait_refs":[{"HashConsedValue":[8392,{"kind":"SelfId","trait_decl_ref":{"regions":[],"skip_binder":{"id":27,"generics":{"regions":[],"types":[{"Deduplicated":8294}],"const_generics":[],"trait_refs":[]}}}}]}]}}},"kind":{"TraitMethod":[27,0]}},{"params":{"regions":[{"index":0,"name":null,"mutability":"Unknown"}],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"next_u64","attr_info":{"attributes":[{"DocComment":" Return the next random `u64`."},{"DocComment":""},{"DocComment":" RNGs must implement at least one method from this trait directly. In"},{"DocComment":" the case this method is not implemented directly, it can be implemented"},{"DocComment":" via [`impls::next_u64_via_u32`] or via [`impls::next_u64_via_fill`]."}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8363}],"output":{"Deduplicated":1072}},"item":{"id":220,"generics":{"regions":[{"Var":{"Bound":[0,0]}}],"types":[{"Deduplicated":8294}],"const_generics":[],"trait_refs":[{"Deduplicated":8392}]}}},"kind":{"TraitMethod":[27,1]}},{"params":{"regions":[{"index":0,"name":null,"mutability":"Unknown"},{"index":1,"name":null,"mutability":"Unknown"}],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"fill_bytes","attr_info":{"attributes":[{"DocComment":" Fill `dest` with random data."},{"DocComment":""},{"DocComment":" RNGs must implement at least one method from this trait directly. In"},{"DocComment":" the case this method is not implemented directly, it can be implemented"},{"DocComment":" via [`impls::fill_bytes_via_next`] or"},{"DocComment":" via [`RngCore::try_fill_bytes`]; if this generator can"},{"DocComment":" fail the implementation must choose how best to handle errors here"},{"DocComment":" (e.g. panic with a descriptive message or log a warning and retry a few"},{"DocComment":" times)."},{"DocComment":""},{"DocComment":" This method should guarantee that `dest` is entirely filled"},{"DocComment":" with new data, and may panic if this is impossible"},{"DocComment":" (e.g. reading past the end of a file that is being used as the"},{"DocComment":" source of randomness)."}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8363},{"HashConsedValue":[4787,{"Ref":[{"Var":{"Bound":[0,1]}},{"Deduplicated":2162},"Mut"]}]}],"output":{"Deduplicated":1108}},"item":{"id":221,"generics":{"regions":[{"Var":{"Bound":[0,0]}},{"Var":{"Bound":[0,1]}}],"types":[{"Deduplicated":8294}],"const_generics":[],"trait_refs":[{"Deduplicated":8392}]}}},"kind":{"TraitMethod":[27,2]}},{"params":{"regions":[{"index":0,"name":null,"mutability":"Unknown"},{"index":1,"name":null,"mutability":"Unknown"}],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"try_fill_bytes","attr_info":{"attributes":[{"DocComment":" Fill `dest` entirely with random data."},{"DocComment":""},{"DocComment":" This is the only method which allows an RNG to report errors while"},{"DocComment":" generating random data thus making this the primary method implemented"},{"DocComment":" by external (true) RNGs (e.g. `OsRng`) which can fail. It may be used"},{"DocComment":" directly to generate keys and to seed (infallible) PRNGs."},{"DocComment":""},{"DocComment":" Other than error handling, this method is identical to [`RngCore::fill_bytes`];"},{"DocComment":" thus this may be implemented using `Ok(self.fill_bytes(dest))` or"},{"DocComment":" `fill_bytes` may be implemented with"},{"DocComment":" `self.try_fill_bytes(dest).unwrap()` or more specific error handling."}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8363},{"Deduplicated":4787}],"output":{"Deduplicated":4813}},"item":{"id":222,"generics":{"regions":[{"Var":{"Bound":[0,0]}},{"Var":{"Bound":[0,1]}}],"types":[{"Deduplicated":8294}],"const_generics":[],"trait_refs":[{"Deduplicated":8392}]}}},"kind":{"TraitMethod":[27,3]}}],"vtable":{"id":{"Adt":51},"generics":{"regions":[],"types":[],"const_generics":[],"trait_refs":[]}}},{"def_id":28,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["convert",0]},{"Ident":["AsRef",0]}],"span":{"data":{"file_id":9,"beg":{"line":219,"col":0},"end":{"line":219,"col":52}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" Used to do a cheap reference-to-reference conversion."},{"DocComment":""},{"DocComment":" This trait is similar to [`AsMut`] which is used for converting between mutable references."},{"DocComment":" If you need to do a costly conversion it is better to implement [`From`] with type"},{"DocComment":" `&T` or write a custom function."},{"DocComment":""},{"DocComment":" # Relation to `Borrow`"},{"DocComment":""},{"DocComment":" `AsRef` has the same signature as [`Borrow`], but [`Borrow`] is different in a few aspects:"},{"DocComment":""},{"DocComment":" - Unlike `AsRef`, [`Borrow`] has a blanket impl for any `T`, and can be used to accept either"},{"DocComment":" a reference or a value. (See also note on `AsRef`'s reflexibility below.)"},{"DocComment":" - [`Borrow`] also requires that [`Hash`], [`Eq`] and [`Ord`] for a borrowed value are"},{"DocComment":" equivalent to those of the owned value. For this reason, if you want to"},{"DocComment":" borrow only a single field of a struct you can implement `AsRef`, but not [`Borrow`]."},{"DocComment":""},{"DocComment":" **Note: This trait must not fail**. If the conversion can fail, use a"},{"DocComment":" dedicated method which returns an [`Option<T>`] or a [`Result<T, E>`]."},{"DocComment":""},{"DocComment":" # Generic Implementations"},{"DocComment":""},{"DocComment":" `AsRef` auto-dereferences if the inner type is a reference or a mutable reference"},{"DocComment":" (e.g.: `foo.as_ref()` will work the same if `foo` has type `&mut Foo` or `&&mut Foo`)."},{"DocComment":""},{"DocComment":" Note that due to historic reasons, the above currently does not hold generally for all"},{"DocComment":" [dereferenceable types], e.g. `foo.as_ref()` will *not* work the same as"},{"DocComment":" `Box::new(foo).as_ref()`. Instead, many smart pointers provide an `as_ref` implementation which"},{"DocComment":" simply returns a reference to the [pointed-to value] (but do not perform a cheap"},{"DocComment":" reference-to-reference conversion for that value). However, [`AsRef::as_ref`] should not be"},{"DocComment":" used for the sole purpose of dereferencing; instead ['`Deref` coercion'] can be used:"},{"DocComment":""},{"DocComment":" [dereferenceable types]: core::ops::Deref"},{"DocComment":" [pointed-to value]: core::ops::Deref::Target"},{"DocComment":" ['`Deref` coercion']: core::ops::Deref#deref-coercion"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" let x = Box::new(5i32);"},{"DocComment":" // Avoid this:"},{"DocComment":" // let y: &i32 = x.as_ref();"},{"DocComment":" // Better just write:"},{"DocComment":" let y: &i32 = &x;"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" Types which implement [`Deref`] should consider implementing `AsRef<T>` as follows:"},{"DocComment":""},{"DocComment":" [`Deref`]: core::ops::Deref"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" # use core::ops::Deref;"},{"DocComment":" # struct SomeType;"},{"DocComment":" # impl Deref for SomeType {"},{"DocComment":" # type Target = [u8];"},{"DocComment":" # fn deref(&self) -> &[u8] {"},{"DocComment":" # &[]"},{"DocComment":" # }"},{"DocComment":" # }"},{"DocComment":" impl<T> AsRef<T> for SomeType"},{"DocComment":" where"},{"DocComment":" T: ?Sized,"},{"DocComment":" <SomeType as Deref>::Target: AsRef<T>,"},{"DocComment":" {"},{"DocComment":" fn as_ref(&self) -> &T {"},{"DocComment":" self.deref().as_ref()"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" # Reflexivity"},{"DocComment":""},{"DocComment":" Ideally, `AsRef` would be reflexive, i.e. there would be an `impl<T: ?Sized> AsRef<T> for T`"},{"DocComment":" with [`as_ref`] simply returning its argument unchanged."},{"DocComment":" Such a blanket implementation is currently *not* provided due to technical restrictions of"},{"DocComment":" Rust's type system (it would be overlapping with another existing blanket implementation for"},{"DocComment":" `&T where T: AsRef<U>` which allows `AsRef` to auto-dereference, see \"Generic Implementations\""},{"DocComment":" above)."},{"DocComment":""},{"DocComment":" [`as_ref`]: AsRef::as_ref"},{"DocComment":""},{"DocComment":" A trivial implementation of `AsRef<T> for T` must be added explicitly for a particular type `T`"},{"DocComment":" where needed or desired. Note, however, that not all types from `std` contain such an"},{"DocComment":" implementation, and those cannot be added by external code due to orphan rules."},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" By using trait bounds we can accept arguments of different types as long as they can be"},{"DocComment":" converted to the specified type `T`."},{"DocComment":""},{"DocComment":" For example: By creating a generic function that takes an `AsRef<str>` we express that we"},{"DocComment":" want to accept all references that can be converted to [`&str`] as an argument."},{"DocComment":" Since both [`String`] and [`&str`] implement `AsRef<str>` we can accept both as input argument."},{"DocComment":""},{"DocComment":" [`&str`]: primitive@str"},{"DocComment":" [`Borrow`]: crate::borrow::Borrow"},{"DocComment":" [`Eq`]: crate::cmp::Eq"},{"DocComment":" [`Ord`]: crate::cmp::Ord"},{"DocComment":" [`String`]: ../../std/string/struct.String.html"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" fn is_hello<T: AsRef<str>>(s: T) {"},{"DocComment":" assert_eq!(\"hello\", s.as_ref());"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" let s = \"hello\";"},{"DocComment":" is_hello(s);"},{"DocComment":""},{"DocComment":" let s = \"hello\".to_string();"},{"DocComment":" is_hello(s);"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"AsRef"},"generics":{"regions":[],"types":[{"index":0,"name":"Self"},{"index":1,"name":"T"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[],"consts":[],"types":[],"methods":[{"params":{"regions":[{"index":0,"name":null,"mutability":"Unknown"}],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"as_ref","attr_info":{"attributes":[{"DocComment":" Converts this type into a shared reference of the (usually inferred) input type."}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8361}],"output":{"Deduplicated":8381}},"item":{"id":223,"generics":{"regions":[{"Var":{"Bound":[0,0]}}],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[{"HashConsedValue":[8393,{"kind":"SelfId","trait_decl_ref":{"regions":[],"skip_binder":{"id":28,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}}}]}]}}},"kind":{"TraitMethod":[28,0]}}],"vtable":{"id":{"Adt":53},"generics":{"regions":[],"types":[{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}},{"def_id":29,"item_meta":{"name":[{"Ident":["ff",0]},{"Ident":["PrimeField",0]}],"span":{"data":{"file_id":21,"beg":{"line":195,"col":0},"end":{"line":195,"col":39}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" This represents an element of a non-binary prime field."}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":null},"generics":{"regions":[],"types":[{"index":0,"name":"Self"},{"index":1,"name":"Self_Repr"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[{"regions":[],"skip_binder":[{"Deduplicated":8295},"Static"]}],"trait_type_constraints":[]},"implied_clauses":[{"clause_id":0,"span":{"data":{"file_id":21,"beg":{"line":195,"col":22},"end":{"line":195,"col":27}},"generated_from_span":null},"origin":"WhereClauseOnTrait","trait_":{"regions":[],"skip_binder":{"id":24,"generics":{"regions":[],"types":[{"Deduplicated":8294}],"const_generics":[],"trait_refs":[]}}}},{"clause_id":1,"span":{"data":{"file_id":21,"beg":{"line":195,"col":30},"end":{"line":195,"col":39}},"generated_from_span":null},"origin":"WhereClauseOnTrait","trait_":{"regions":[],"skip_binder":{"id":7,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":1072}],"const_generics":[],"trait_refs":[]}}}},{"clause_id":2,"span":{"data":{"file_id":21,"beg":{"line":198,"col":15},"end":{"line":198,"col":19}},"generated_from_span":null},"origin":{"TraitItem":0},"trait_":{"regions":[],"skip_binder":{"id":3,"generics":{"regions":[],"types":[{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}}},{"clause_id":3,"span":{"data":{"file_id":21,"beg":{"line":198,"col":22},"end":{"line":198,"col":29}},"generated_from_span":null},"origin":{"TraitItem":0},"trait_":{"regions":[],"skip_binder":{"id":23,"generics":{"regions":[],"types":[{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}}},{"clause_id":4,"span":{"data":{"file_id":21,"beg":{"line":198,"col":32},"end":{"line":198,"col":36}},"generated_from_span":null},"origin":{"TraitItem":0},"trait_":{"regions":[],"skip_binder":{"id":25,"generics":{"regions":[],"types":[{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}}},{"clause_id":5,"span":{"data":{"file_id":21,"beg":{"line":198,"col":39},"end":{"line":198,"col":43}},"generated_from_span":null},"origin":{"TraitItem":0},"trait_":{"regions":[],"skip_binder":{"id":26,"generics":{"regions":[],"types":[{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}}},{"clause_id":6,"span":{"data":{"file_id":21,"beg":{"line":198,"col":56},"end":{"line":198,"col":67}},"generated_from_span":null},"origin":{"TraitItem":0},"trait_":{"regions":[],"skip_binder":{"id":28,"generics":{"regions":[],"types":[{"Deduplicated":8295},{"Deduplicated":2162}],"const_generics":[],"trait_refs":[]}}}},{"clause_id":7,"span":{"data":{"file_id":21,"beg":{"line":198,"col":70},"end":{"line":198,"col":81}},"generated_from_span":null},"origin":{"TraitItem":0},"trait_":{"regions":[],"skip_binder":{"id":30,"generics":{"regions":[],"types":[{"Deduplicated":8295},{"Deduplicated":2162}],"const_generics":[],"trait_refs":[]}}}}],"consts":[{"name":"MODULUS","attr_info":{"attributes":[{"DocComment":" Modulus of the field written as a string for debugging purposes."},{"DocComment":""},{"DocComment":" The encoding of the modulus is implementation-specific. Generic users of the"},{"DocComment":" `PrimeField` trait should treat this string as opaque."}],"inline":null,"rename":null,"public":true},"ty":{"Deduplicated":2250},"default":null},{"name":"NUM_BITS","attr_info":{"attributes":[{"DocComment":" How many bits are needed to represent an element of this field."}],"inline":null,"rename":null,"public":true},"ty":{"Deduplicated":1834},"default":null},{"name":"CAPACITY","attr_info":{"attributes":[{"DocComment":" How many bits of information can be reliably stored in the field element."},{"DocComment":""},{"DocComment":" This is usually `Self::NUM_BITS - 1`."}],"inline":null,"rename":null,"public":true},"ty":{"Deduplicated":1834},"default":null},{"name":"TWO_INV","attr_info":{"attributes":[{"DocComment":" Inverse of $2$ in the field."}],"inline":null,"rename":null,"public":true},"ty":{"Deduplicated":8294},"default":null},{"name":"MULTIPLICATIVE_GENERATOR","attr_info":{"attributes":[{"DocComment":" A fixed multiplicative generator of `modulus - 1` order. This element must also be"},{"DocComment":" a quadratic nonresidue."},{"DocComment":""},{"DocComment":" It can be calculated using [SageMath] as `GF(modulus).primitive_element()`."},{"DocComment":""},{"DocComment":" Implementations of this trait MUST ensure that this is the generator used to"},{"DocComment":" derive `Self::ROOT_OF_UNITY`."},{"DocComment":""},{"DocComment":" [SageMath]: https://www.sagemath.org/"}],"inline":null,"rename":null,"public":true},"ty":{"Deduplicated":8294},"default":null},{"name":"S","attr_info":{"attributes":[{"DocComment":" An integer `s` satisfying the equation `2^s * t = modulus - 1` with `t` odd."},{"DocComment":""},{"DocComment":" This is the number of leading zero bits in the little-endian bit representation of"},{"DocComment":" `modulus - 1`."}],"inline":null,"rename":null,"public":true},"ty":{"Deduplicated":1834},"default":null},{"name":"ROOT_OF_UNITY","attr_info":{"attributes":[{"DocComment":" The `2^s` root of unity."},{"DocComment":""},{"DocComment":" It can be calculated by exponentiating `Self::MULTIPLICATIVE_GENERATOR` by `t`,"},{"DocComment":" where `t = (modulus - 1) >> Self::S`."}],"inline":null,"rename":null,"public":true},"ty":{"Deduplicated":8294},"default":null},{"name":"ROOT_OF_UNITY_INV","attr_info":{"attributes":[{"DocComment":" Inverse of [`Self::ROOT_OF_UNITY`]."}],"inline":null,"rename":null,"public":true},"ty":{"Deduplicated":8294},"default":null},{"name":"DELTA","attr_info":{"attributes":[{"DocComment":" Generator of the `t-order` multiplicative subgroup."},{"DocComment":""},{"DocComment":" It can be calculated by exponentiating [`Self::MULTIPLICATIVE_GENERATOR`] by `2^s`,"},{"DocComment":" where `s` is [`Self::S`]."}],"inline":null,"rename":null,"public":true},"ty":{"Deduplicated":8294},"default":null}],"types":[null],"methods":[null,{"params":{"regions":[],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"from_u128","attr_info":{"attributes":[{"DocComment":" Obtains a field element congruent to the integer `v`."},{"DocComment":""},{"DocComment":" For fields where `Self::CAPACITY >= 128`, this is injective and will produce a"},{"DocComment":" unique field element."},{"DocComment":""},{"DocComment":" For fields where `Self::CAPACITY < 128`, this is surjective; some field elements"},{"DocComment":" will be produced by multiple values of `v`."},{"DocComment":""},{"DocComment":" If you want to deterministically sample a field element representing a value, use"},{"DocComment":" [`FromUniformBytes`] instead."}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":2226}],"output":{"Deduplicated":8294}},"item":{"id":102,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[{"HashConsedValue":[8394,{"kind":"SelfId","trait_decl_ref":{"regions":[],"skip_binder":{"id":29,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}}}]}]}}},"kind":{"TraitMethod":[29,1]}},{"params":{"regions":[],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"from_repr","attr_info":{"attributes":[{"DocComment":" Attempts to convert a byte representation of a field element into an element of"},{"DocComment":" this prime field, failing if the input is not canonical (is not smaller than the"},{"DocComment":" field's modulus)."},{"DocComment":""},{"DocComment":" The byte representation is interpreted with the same endianness as elements"},{"DocComment":" returned by [`PrimeField::to_repr`]."}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8295}],"output":{"Deduplicated":8390}},"item":{"id":103,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[{"Deduplicated":8394}]}}},"kind":{"TraitMethod":[29,2]}},null,{"params":{"regions":[{"index":0,"name":null,"mutability":"Unknown"}],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"to_repr","attr_info":{"attributes":[{"DocComment":" Converts an element of the prime field into the standard byte representation for"},{"DocComment":" this field."},{"DocComment":""},{"DocComment":" The endianness of the byte representation is implementation-specific. Generic"},{"DocComment":" encodings of field elements should be treated as opaque."}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8361}],"output":{"Deduplicated":8295}},"item":{"id":105,"generics":{"regions":[{"Var":{"Bound":[0,0]}}],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[{"Deduplicated":8394}]}}},"kind":{"TraitMethod":[29,4]}},{"params":{"regions":[{"index":0,"name":null,"mutability":"Unknown"}],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"is_odd","attr_info":{"attributes":[{"DocComment":" Returns true iff this element is odd."}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8361}],"output":{"Deduplicated":1250}},"item":{"id":106,"generics":{"regions":[{"Var":{"Bound":[0,0]}}],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[{"Deduplicated":8394}]}}},"kind":{"TraitMethod":[29,5]}},null],"vtable":null},{"def_id":30,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["convert",0]},{"Ident":["AsMut",0]}],"span":{"data":{"file_id":9,"beg":{"line":371,"col":0},"end":{"line":371,"col":52}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" Used to do a cheap mutable-to-mutable reference conversion."},{"DocComment":""},{"DocComment":" This trait is similar to [`AsRef`] but used for converting between mutable"},{"DocComment":" references. If you need to do a costly conversion it is better to"},{"DocComment":" implement [`From`] with type `&mut T` or write a custom function."},{"DocComment":""},{"DocComment":" **Note: This trait must not fail**. If the conversion can fail, use a"},{"DocComment":" dedicated method which returns an [`Option<T>`] or a [`Result<T, E>`]."},{"DocComment":""},{"DocComment":" # Generic Implementations"},{"DocComment":""},{"DocComment":" `AsMut` auto-dereferences if the inner type is a mutable reference"},{"DocComment":" (e.g.: `foo.as_mut()` will work the same if `foo` has type `&mut Foo` or `&mut &mut Foo`)."},{"DocComment":""},{"DocComment":" Note that due to historic reasons, the above currently does not hold generally for all"},{"DocComment":" [mutably dereferenceable types], e.g. `foo.as_mut()` will *not* work the same as"},{"DocComment":" `Box::new(foo).as_mut()`. Instead, many smart pointers provide an `as_mut` implementation which"},{"DocComment":" simply returns a reference to the [pointed-to value] (but do not perform a cheap"},{"DocComment":" reference-to-reference conversion for that value). However, [`AsMut::as_mut`] should not be"},{"DocComment":" used for the sole purpose of mutable dereferencing; instead ['`Deref` coercion'] can be used:"},{"DocComment":""},{"DocComment":" [mutably dereferenceable types]: core::ops::DerefMut"},{"DocComment":" [pointed-to value]: core::ops::Deref::Target"},{"DocComment":" ['`Deref` coercion']: core::ops::DerefMut#mutable-deref-coercion"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" let mut x = Box::new(5i32);"},{"DocComment":" // Avoid this:"},{"DocComment":" // let y: &mut i32 = x.as_mut();"},{"DocComment":" // Better just write:"},{"DocComment":" let y: &mut i32 = &mut x;"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" Types which implement [`DerefMut`] should consider to add an implementation of `AsMut<T>` as"},{"DocComment":" follows:"},{"DocComment":""},{"DocComment":" [`DerefMut`]: core::ops::DerefMut"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" # use core::ops::{Deref, DerefMut};"},{"DocComment":" # struct SomeType;"},{"DocComment":" # impl Deref for SomeType {"},{"DocComment":" # type Target = [u8];"},{"DocComment":" # fn deref(&self) -> &[u8] {"},{"DocComment":" # &[]"},{"DocComment":" # }"},{"DocComment":" # }"},{"DocComment":" # impl DerefMut for SomeType {"},{"DocComment":" # fn deref_mut(&mut self) -> &mut [u8] {"},{"DocComment":" # &mut []"},{"DocComment":" # }"},{"DocComment":" # }"},{"DocComment":" impl<T> AsMut<T> for SomeType"},{"DocComment":" where"},{"DocComment":" <SomeType as Deref>::Target: AsMut<T>,"},{"DocComment":" {"},{"DocComment":" fn as_mut(&mut self) -> &mut T {"},{"DocComment":" self.deref_mut().as_mut()"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" # Reflexivity"},{"DocComment":""},{"DocComment":" Ideally, `AsMut` would be reflexive, i.e. there would be an `impl<T: ?Sized> AsMut<T> for T`"},{"DocComment":" with [`as_mut`] simply returning its argument unchanged."},{"DocComment":" Such a blanket implementation is currently *not* provided due to technical restrictions of"},{"DocComment":" Rust's type system (it would be overlapping with another existing blanket implementation for"},{"DocComment":" `&mut T where T: AsMut<U>` which allows `AsMut` to auto-dereference, see \"Generic"},{"DocComment":" Implementations\" above)."},{"DocComment":""},{"DocComment":" [`as_mut`]: AsMut::as_mut"},{"DocComment":""},{"DocComment":" A trivial implementation of `AsMut<T> for T` must be added explicitly for a particular type `T`"},{"DocComment":" where needed or desired. Note, however, that not all types from `std` contain such an"},{"DocComment":" implementation, and those cannot be added by external code due to orphan rules."},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" Using `AsMut` as trait bound for a generic function, we can accept all mutable references that"},{"DocComment":" can be converted to type `&mut T`. Unlike [dereference], which has a single [target type],"},{"DocComment":" there can be multiple implementations of `AsMut` for a type. In particular, `Vec<T>` implements"},{"DocComment":" both `AsMut<Vec<T>>` and `AsMut<[T]>`."},{"DocComment":""},{"DocComment":" In the following, the example functions `caesar` and `null_terminate` provide a generic"},{"DocComment":" interface which works with any type that can be converted by cheap mutable-to-mutable conversion"},{"DocComment":" into a byte slice (`[u8]`) or a byte vector (`Vec<u8>`), respectively."},{"DocComment":""},{"DocComment":" [dereference]: core::ops::DerefMut"},{"DocComment":" [target type]: core::ops::Deref::Target"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" struct Document {"},{"DocComment":" info: String,"},{"DocComment":" content: Vec<u8>,"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl<T: ?Sized> AsMut<T> for Document"},{"DocComment":" where"},{"DocComment":" Vec<u8>: AsMut<T>,"},{"DocComment":" {"},{"DocComment":" fn as_mut(&mut self) -> &mut T {"},{"DocComment":" self.content.as_mut()"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" fn caesar<T: AsMut<[u8]>>(data: &mut T, key: u8) {"},{"DocComment":" for byte in data.as_mut() {"},{"DocComment":" *byte = byte.wrapping_add(key);"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" fn null_terminate<T: AsMut<Vec<u8>>>(data: &mut T) {"},{"DocComment":" // Using a non-generic inner function, which contains most of the"},{"DocComment":" // functionality, helps to minimize monomorphization overhead."},{"DocComment":" fn doit(data: &mut Vec<u8>) {"},{"DocComment":" let len = data.len();"},{"DocComment":" if len == 0 || data[len-1] != 0 {"},{"DocComment":" data.push(0);"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":" doit(data.as_mut());"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" fn main() {"},{"DocComment":" let mut v: Vec<u8> = vec![1, 2, 3];"},{"DocComment":" caesar(&mut v, 5);"},{"DocComment":" assert_eq!(v, [6, 7, 8]);"},{"DocComment":" null_terminate(&mut v);"},{"DocComment":" assert_eq!(v, [6, 7, 8, 0]);"},{"DocComment":" let mut doc = Document {"},{"DocComment":" info: String::from(\"Example\"),"},{"DocComment":" content: vec![17, 19, 8],"},{"DocComment":" };"},{"DocComment":" caesar(&mut doc, 1);"},{"DocComment":" assert_eq!(doc.content, [18, 20, 9]);"},{"DocComment":" null_terminate(&mut doc);"},{"DocComment":" assert_eq!(doc.content, [18, 20, 9, 0]);"},{"DocComment":" }"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" Note, however, that APIs don't need to be generic. In many cases taking a `&mut [u8]` or"},{"DocComment":" `&mut Vec<u8>`, for example, is the better choice (callers need to pass the correct type then)."}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"AsMut"},"generics":{"regions":[],"types":[{"index":0,"name":"Self"},{"index":1,"name":"T"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[],"consts":[],"types":[],"methods":[{"params":{"regions":[{"index":0,"name":null,"mutability":"Unknown"}],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"as_mut","attr_info":{"attributes":[{"DocComment":" Converts this type into a mutable reference of the (usually inferred) input type."}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8363}],"output":{"HashConsedValue":[8395,{"Ref":[{"Var":{"Bound":[0,0]}},{"Deduplicated":8295},"Mut"]}]}},"item":{"id":230,"generics":{"regions":[{"Var":{"Bound":[0,0]}}],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[{"HashConsedValue":[8396,{"kind":"SelfId","trait_decl_ref":{"regions":[],"skip_binder":{"id":30,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}}}]}]}}},"kind":{"TraitMethod":[30,0]}}],"vtable":{"id":{"Adt":54},"generics":{"regions":[],"types":[{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}},{"def_id":31,"item_meta":{"name":[{"Ident":["pasta_curves",0]},{"Ident":["arithmetic",0]},{"Ident":["fields",0]},{"Ident":["SqrtTableHelpers",0]}],"span":{"data":{"file_id":24,"beg":{"line":20,"col":0},"end":{"line":29,"col":1}},"generated_from_span":null},"source_text":"pub(crate) trait SqrtTableHelpers: ff::PrimeField {\n /// Raise this field element to the power $(t-1)/2$.\n ///\n /// Field implementations may override this to use an efficient addition chain.\n fn pow_by_t_minus1_over2(&self) -> Self;\n\n /// Gets the lower 32 bits of this field element when expressed\n /// canonically.\n fn get_lower_32(&self) -> u32;\n}","attr_info":{"attributes":[{"DocComment":" An internal trait that exposes additional operations related to calculating square roots of"},{"DocComment":" prime-order finite 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to the power $(t-1)/2$."},{"DocComment":""},{"DocComment":" Field implementations may override this to use an efficient addition chain."}],"inline":null,"rename":null,"public":false},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8361}],"output":{"Deduplicated":8294}},"item":{"id":249,"generics":{"regions":[{"Var":{"Bound":[0,0]}}],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[{"HashConsedValue":[8397,{"kind":"SelfId","trait_decl_ref":{"regions":[],"skip_binder":{"id":31,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}}}]}]}}},"kind":{"TraitMethod":[31,0]}},{"params":{"regions":[{"index":0,"name":null,"mutability":"Unknown"}],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"get_lower_32","attr_info":{"attributes":[{"DocComment":" Gets the lower 32 bits of this field element when expressed"},{"DocComment":" canonically."}],"inline":null,"rename":null,"public":false},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8361}],"output":{"Deduplicated":1834}},"item":{"id":250,"generics":{"regions":[{"Var":{"Bound":[0,0]}}],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[{"Deduplicated":8397}]}}},"kind":{"TraitMethod":[31,1]}}],"vtable":null},{"def_id":32,"item_meta":{"name":[{"Ident":["ff",0]},{"Ident":["WithSmallOrderMulGroup",0]}],"span":{"data":{"file_id":21,"beg":{"line":358,"col":0},"end":{"line":358,"col":57}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" The subset of prime-order fields such that `(modulus - 1)` is divisible by `N`."},{"DocComment":""},{"DocComment":" If `N` is prime, there will be `N - 1` valid choices of [`Self::ZETA`]. Similarly to"},{"DocComment":" [`PrimeField::MULTIPLICATIVE_GENERATOR`], the specific choice does not matter, as long"},{"DocComment":" as the choice is consistent across all uses of the field."}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":null},"generics":{"regions":[],"types":[{"index":0,"name":"Self"},{"index":1,"name":"Self_Clause0_Repr"}],"const_generics":[{"index":0,"name":"N","ty":{"Deduplicated":1894}}],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[{"clause_id":0,"span":{"data":{"file_id":21,"beg":{"line":358,"col":47},"end":{"line":358,"col":57}},"generated_from_span":null},"origin":"WhereClauseOnTrait","trait_":{"regions":[],"skip_binder":{"id":29,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}}}],"consts":[{"name":"ZETA","attr_info":{"attributes":[{"DocComment":" A field element of small multiplicative order $N$."},{"DocComment":""},{"DocComment":" The presence of this element allows you to perform (certain types of)"},{"DocComment":" endomorphisms on some elliptic curves."},{"DocComment":""},{"DocComment":" It can be calculated using [SageMath] as"},{"DocComment":" `GF(modulus).primitive_element() ^ ((modulus - 1) // N)`."},{"DocComment":" Choosing the element of order $N$ that is smallest, when considered"},{"DocComment":" as an integer, may help to ensure consistency."},{"DocComment":""},{"DocComment":" [SageMath]: https://www.sagemath.org/"}],"inline":null,"rename":null,"public":true},"ty":{"Deduplicated":8294},"default":null}],"types":[],"methods":[],"vtable":null},{"def_id":33,"item_meta":{"name":[{"Ident":["ff",0]},{"Ident":["FromUniformBytes",0]}],"span":{"data":{"file_id":21,"beg":{"line":444,"col":0},"end":{"line":444,"col":54}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" Trait for constructing a [`PrimeField`] element from a fixed-length uniform byte"},{"DocComment":" array."},{"DocComment":""},{"DocComment":" \"Uniform\" means that the byte array's contents must be indistinguishable from the"},{"DocComment":" [discrete uniform distribution]. Suitable byte arrays can be obtained:"},{"DocComment":" - from a cryptographically-secure randomness source (which makes this constructor"},{"DocComment":" equivalent to [`Field::random`])."},{"DocComment":" - from a cryptographic hash function output, which enables a \"random\" field element to"},{"DocComment":" be selected deterministically. This is the primary use case for `FromUniformBytes`."},{"DocComment":""},{"DocComment":" The length `N` of the byte array is chosen by the trait implementer such that the loss"},{"DocComment":" of uniformity in the mapping from byte arrays to field elements is cryptographically"},{"DocComment":" negligible."},{"DocComment":""},{"DocComment":" [discrete uniform distribution]: https://en.wikipedia.org/wiki/Discrete_uniform_distribution"},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" # #[cfg(feature = \"derive\")] {"},{"DocComment":" # // Fake this so we don't actually need a dev-dependency on bls12_381."},{"DocComment":" # mod bls12_381 {"},{"DocComment":" # use ff::{Field, PrimeField};"},{"DocComment":" #"},{"DocComment":" # #[derive(PrimeField)]"},{"DocComment":" # #[PrimeFieldModulus = \"52435875175126190479447740508185965837690552500527637822603658699938581184513\"]"},{"DocComment":" # #[PrimeFieldGenerator = \"7\"]"},{"DocComment":" # #[PrimeFieldReprEndianness = \"little\"]"},{"DocComment":" # pub struct Scalar([u64; 4]);"},{"DocComment":" #"},{"DocComment":" # impl ff::FromUniformBytes<64> for Scalar {"},{"DocComment":" # fn from_uniform_bytes(_bytes: &[u8; 64]) -> Self {"},{"DocComment":" # // Fake impl for doctest"},{"DocComment":" # Scalar::ONE"},{"DocComment":" # }"},{"DocComment":" # }"},{"DocComment":" # }"},{"DocComment":" #"},{"DocComment":" use blake2b_simd::blake2b;"},{"DocComment":" use bls12_381::Scalar;"},{"DocComment":" use ff::FromUniformBytes;"},{"DocComment":""},{"DocComment":" // `bls12_381::Scalar` implements `FromUniformBytes<64>`, and BLAKE2b (by default)"},{"DocComment":" // produces a 64-byte hash."},{"DocComment":" let hash = blake2b(b\"Some message\");"},{"DocComment":" let val = Scalar::from_uniform_bytes(hash.as_array());"},{"DocComment":" # }"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" # Implementing `FromUniformBytes`"},{"DocComment":""},{"DocComment":" [`Self::from_uniform_bytes`] should always be implemented by interpreting the provided"},{"DocComment":" byte array as the little endian unsigned encoding of an integer, and then reducing that"},{"DocComment":" integer modulo the field modulus."},{"DocComment":""},{"DocComment":" For security, `N` must be chosen so that `N * 8 >= Self::NUM_BITS + 128`. A larger"},{"DocComment":" value of `N` may be chosen for convenience; for example, for a field with a 255-bit"},{"DocComment":" modulus, `N = 64` is convenient as it matches the output length of several common"},{"DocComment":" cryptographic hash functions (such as SHA-512 and BLAKE2b)."},{"DocComment":""},{"DocComment":" ## Trait design"},{"DocComment":""},{"DocComment":" This trait exists because `PrimeField::from_uniform_bytes([u8; N])` cannot currently"},{"DocComment":" exist (trait methods cannot use associated constants in the const positions of their"},{"DocComment":" type signature, and we do not want `PrimeField` to require a generic const parameter)."},{"DocComment":" However, this has the side-effect that `FromUniformBytes` can be implemented multiple"},{"DocComment":" times for different values of `N`. Most implementations of [`PrimeField`] should only"},{"DocComment":" need to implement `FromUniformBytes` trait for one value of `N` (chosen following the"},{"DocComment":" above considerations); if you find yourself needing to implement it multiple times,"},{"DocComment":" please [let us know about your use case](https://github.com/zkcrypto/ff/issues/new) so"},{"DocComment":" we can take it into consideration for future evolutions of the `ff` traits."}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":null},"generics":{"regions":[],"types":[{"index":0,"name":"Self"},{"index":1,"name":"Self_Clause0_Repr"}],"const_generics":[{"index":0,"name":"N","ty":{"Deduplicated":1073}}],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[{"clause_id":0,"span":{"data":{"file_id":21,"beg":{"line":444,"col":44},"end":{"line":444,"col":54}},"generated_from_span":null},"origin":"WhereClauseOnTrait","trait_":{"regions":[],"skip_binder":{"id":29,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}}}],"consts":[],"types":[],"methods":[{"params":{"regions":[{"index":0,"name":null,"mutability":"Unknown"}],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"from_uniform_bytes","attr_info":{"attributes":[{"DocComment":" Returns a field element that is congruent to the provided little endian unsigned"},{"DocComment":" byte representation of an integer."}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"HashConsedValue":[8399,{"Ref":[{"Var":{"Bound":[0,0]}},{"Deduplicated":8398},"Shared"]}]}],"output":{"Deduplicated":8294}},"item":{"id":252,"generics":{"regions":[{"Var":{"Bound":[0,0]}}],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[{"kind":{"Var":{"Free":0}},"ty":{"Deduplicated":1073}}],"trait_refs":[{"HashConsedValue":[8400,{"kind":"SelfId","trait_decl_ref":{"regions":[],"skip_binder":{"id":33,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[{"kind":{"Var":{"Free":0}},"ty":{"Deduplicated":1073}}],"trait_refs":[]}}}}]}]}}},"kind":{"TraitMethod":[33,0]}}],"vtable":null},{"def_id":34,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["num",0]},{"Ident":["nonzero",0]},{"Ident":["ZeroablePrimitive",0]}],"span":{"data":{"file_id":28,"beg":{"line":34,"col":0},"end":{"line":34,"col":66}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" A marker trait for primitive types which can be zero."},{"DocComment":""},{"DocComment":" This is an implementation detail for <code>[NonZero]\\<T></code> which may disappear or be replaced at any time."},{"DocComment":""},{"DocComment":" # Safety"},{"DocComment":""},{"DocComment":" Types implementing this trait must be primitives that are valid when zeroed."},{"DocComment":""},{"DocComment":" The associated `Self::NonZeroInner` type must have the same size+align as `Self`,"},{"DocComment":" but with a niche and bit validity making it so the following `transmutes` are sound:"},{"DocComment":""},{"DocComment":" - `Self::NonZeroInner` to `Option<Self::NonZeroInner>`"},{"DocComment":" - `Option<Self::NonZeroInner>` to `Self`"},{"DocComment":""},{"DocComment":" (And, consequently, `Self::NonZeroInner` to `Self`.)"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":null},"generics":{"regions":[],"types":[{"index":0,"name":"Self"},{"index":1,"name":"Self_NonZeroInner"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[{"clause_id":0,"span":{"data":{"file_id":28,"beg":{"line":34,"col":44},"end":{"line":34,"col":48}},"generated_from_span":null},"origin":"WhereClauseOnTrait","trait_":{"regions":[],"skip_binder":{"id":3,"generics":{"regions":[],"types":[{"Deduplicated":8294}],"const_generics":[],"trait_refs":[]}}}},{"clause_id":1,"span":{"data":{"file_id":28,"beg":{"line":34,"col":51},"end":{"line":34,"col":66}},"generated_from_span":null},"origin":"WhereClauseOnTrait","trait_":{"regions":[],"skip_binder":{"id":50,"generics":{"regions":[],"types":[{"Deduplicated":8294}],"const_generics":[],"trait_refs":[]}}}},{"clause_id":2,"span":{"data":{"file_id":28,"beg":{"line":36,"col":31},"end":{"line":36,"col":35}},"generated_from_span":null},"origin":{"TraitItem":0},"trait_":{"regions":[],"skip_binder":{"id":3,"generics":{"regions":[],"types":[{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}}}],"consts":[],"types":[null],"methods":[],"vtable":null},{"def_id":35,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["iter",0]},{"Ident":["traits",0]},{"Ident":["collect",0]},{"Ident":["IntoIterator",0]}],"span":{"data":{"file_id":32,"beg":{"line":283,"col":0},"end":{"line":283,"col":28}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" Conversion into an [`Iterator`]."},{"DocComment":""},{"DocComment":" By implementing `IntoIterator` for a type, you define how it will be"},{"DocComment":" converted to an iterator. This is common for types which describe a"},{"DocComment":" collection of some kind."},{"DocComment":""},{"DocComment":" One benefit of implementing `IntoIterator` is that your type will [work"},{"DocComment":" with Rust's `for` loop syntax](crate::iter#for-loops-and-intoiterator)."},{"DocComment":""},{"DocComment":" See also: [`FromIterator`]."},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" Basic usage:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" let v = [1, 2, 3];"},{"DocComment":" let mut iter = v.into_iter();"},{"DocComment":""},{"DocComment":" assert_eq!(Some(1), iter.next());"},{"DocComment":" assert_eq!(Some(2), iter.next());"},{"DocComment":" assert_eq!(Some(3), iter.next());"},{"DocComment":" assert_eq!(None, iter.next());"},{"DocComment":" ```"},{"DocComment":" Implementing `IntoIterator` for your type:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" // A sample collection, that's just a wrapper over Vec<T>"},{"DocComment":" #[derive(Debug)]"},{"DocComment":" struct MyCollection(Vec<i32>);"},{"DocComment":""},{"DocComment":" // Let's give it some methods so we can create one and add things"},{"DocComment":" // to it."},{"DocComment":" impl MyCollection {"},{"DocComment":" fn new() -> MyCollection {"},{"DocComment":" MyCollection(Vec::new())"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" fn add(&mut self, elem: i32) {"},{"DocComment":" self.0.push(elem);"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" // and we'll implement IntoIterator"},{"DocComment":" impl IntoIterator for MyCollection {"},{"DocComment":" type Item = i32;"},{"DocComment":" type IntoIter = std::vec::IntoIter<Self::Item>;"},{"DocComment":""},{"DocComment":" fn into_iter(self) -> Self::IntoIter {"},{"DocComment":" self.0.into_iter()"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" // Now we can make a new collection..."},{"DocComment":" let mut c = MyCollection::new();"},{"DocComment":""},{"DocComment":" // ... add some stuff to it ..."},{"DocComment":" c.add(0);"},{"DocComment":" c.add(1);"},{"DocComment":" c.add(2);"},{"DocComment":""},{"DocComment":" // ... and then turn it into an Iterator:"},{"DocComment":" for (i, n) in c.into_iter().enumerate() {"},{"DocComment":" assert_eq!(i as i32, n);"},{"DocComment":" }"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" It is common to use `IntoIterator` as a trait bound. This allows"},{"DocComment":" the input collection type to change, so long as it is still an"},{"DocComment":" iterator. Additional bounds can be specified by restricting on"},{"DocComment":" `Item`:"},{"DocComment":""},{"DocComment":" ```rust"},{"DocComment":" fn collect_as_strings<T>(collection: T) -> Vec<String>"},{"DocComment":" where"},{"DocComment":" T: IntoIterator,"},{"DocComment":" T::Item: std::fmt::Debug,"},{"DocComment":" {"},{"DocComment":" collection"},{"DocComment":" .into_iter()"},{"DocComment":" .map(|item| format!(\"{item:?}\"))"},{"DocComment":" .collect()"},{"DocComment":" }"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"IntoIterator"},"generics":{"regions":[],"types":[{"index":0,"name":"Self"},{"index":1,"name":"Self_Item"},{"index":2,"name":"Self_IntoIter"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[{"clause_id":0,"span":{"data":{"file_id":32,"beg":{"line":291,"col":19},"end":{"line":291,"col":46}},"generated_from_span":null},"origin":{"TraitItem":1},"trait_":{"regions":[],"skip_binder":{"id":21,"generics":{"regions":[],"types":[{"Deduplicated":8348},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}}}],"consts":[],"types":[null,null],"methods":[{"params":{"regions":[],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"into_iter","attr_info":{"attributes":[{"DocComment":" Creates an iterator from a value."},{"DocComment":""},{"DocComment":" See the [module-level documentation] for more."},{"DocComment":""},{"DocComment":" [module-level documentation]: crate::iter"},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" let v = [1, 2, 3];"},{"DocComment":" let mut iter = v.into_iter();"},{"DocComment":""},{"DocComment":" assert_eq!(Some(1), iter.next());"},{"DocComment":" assert_eq!(Some(2), iter.next());"},{"DocComment":" assert_eq!(Some(3), iter.next());"},{"DocComment":" assert_eq!(None, iter.next());"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8294}],"output":{"Deduplicated":8348}},"item":{"id":255,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295},{"Deduplicated":8348}],"const_generics":[],"trait_refs":[{"HashConsedValue":[8401,{"kind":"SelfId","trait_decl_ref":{"regions":[],"skip_binder":{"id":35,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295},{"Deduplicated":8348}],"const_generics":[],"trait_refs":[]}}}}]}]}}},"kind":{"TraitMethod":[35,0]}}],"vtable":{"id":{"Adt":58},"generics":{"regions":[],"types":[{"Deduplicated":8295},{"Deduplicated":8348}],"const_generics":[],"trait_refs":[]}}},{"def_id":36,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["ops",0]},{"Ident":["function",0]},{"Ident":["FnMut",0]}],"span":{"data":{"file_id":36,"beg":{"line":163,"col":0},"end":{"line":163,"col":48}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" The version of the call operator that takes a mutable receiver."},{"DocComment":""},{"DocComment":" Instances of `FnMut` can be called repeatedly and may mutate state."},{"DocComment":""},{"DocComment":" `FnMut` is implemented automatically by closures which take mutable"},{"DocComment":" references to captured variables, as well as all types that implement"},{"DocComment":" [`Fn`], e.g., (safe) [function pointers] (since `FnMut` is a supertrait of"},{"DocComment":" [`Fn`]). Additionally, for any type `F` that implements `FnMut`, `&mut F`"},{"DocComment":" implements `FnMut`, too."},{"DocComment":""},{"DocComment":" Since [`FnOnce`] is a supertrait of `FnMut`, any instance of `FnMut` can be"},{"DocComment":" used where a [`FnOnce`] is expected, and since [`Fn`] is a subtrait of"},{"DocComment":" `FnMut`, any instance of [`Fn`] can be used where `FnMut` is expected."},{"DocComment":""},{"DocComment":" Use `FnMut` as a bound when you want to accept a parameter of function-like"},{"DocComment":" type and need to call it repeatedly, while allowing it to mutate state."},{"DocComment":" If you don't want the parameter to mutate state, use [`Fn`] as a"},{"DocComment":" bound; if you don't need to call it repeatedly, use [`FnOnce`]."},{"DocComment":""},{"DocComment":" See the [chapter on closures in *The Rust Programming Language*][book] for"},{"DocComment":" some more information on this topic."},{"DocComment":""},{"DocComment":" Also of note is the special syntax for `Fn` traits (e.g."},{"DocComment":" `Fn(usize, bool) -> usize`). Those interested in the technical details of"},{"DocComment":" this can refer to [the relevant section in the *Rustonomicon*][nomicon]."},{"DocComment":""},{"DocComment":" [book]: ../../book/ch13-01-closures.html"},{"DocComment":" [function pointers]: fn"},{"DocComment":" [nomicon]: ../../nomicon/hrtb.html"},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" ## Calling a mutably capturing closure"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" let mut x = 5;"},{"DocComment":" {"},{"DocComment":" let mut square_x = || x *= x;"},{"DocComment":" square_x();"},{"DocComment":" }"},{"DocComment":" assert_eq!(x, 25);"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" ## Using a `FnMut` parameter"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" fn do_twice<F>(mut func: F)"},{"DocComment":" where F: FnMut()"},{"DocComment":" {"},{"DocComment":" func();"},{"DocComment":" func();"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" let mut x: usize = 1;"},{"DocComment":" {"},{"DocComment":" let add_two_to_x = || x += 2;"},{"DocComment":" do_twice(add_two_to_x);"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" assert_eq!(x, 5);"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"fn_mut"},"generics":{"regions":[],"types":[{"index":0,"name":"Self"},{"index":1,"name":"Args"},{"index":2,"name":"Self_Clause0_Output"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[{"clause_id":0,"span":{"data":{"file_id":36,"beg":{"line":163,"col":36},"end":{"line":163,"col":48}},"generated_from_span":null},"origin":"WhereClauseOnTrait","trait_":{"regions":[],"skip_binder":{"id":37,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295},{"Deduplicated":8348}],"const_generics":[],"trait_refs":[]}}}}],"consts":[],"types":[],"methods":[{"params":{"regions":[{"index":0,"name":null,"mutability":"Unknown"}],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"call_mut","attr_info":{"attributes":[{"DocComment":" Performs the call operation."}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":{"Other":"rust-call"},"inputs":[{"Deduplicated":8363},{"Deduplicated":8295}],"output":{"Deduplicated":8348}},"item":{"id":256,"generics":{"regions":[{"Var":{"Bound":[0,0]}}],"types":[{"Deduplicated":8294},{"Deduplicated":8295},{"Deduplicated":8348}],"const_generics":[],"trait_refs":[{"HashConsedValue":[8402,{"kind":"SelfId","trait_decl_ref":{"regions":[],"skip_binder":{"id":36,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295},{"Deduplicated":8348}],"const_generics":[],"trait_refs":[]}}}}]}]}}},"kind":{"TraitMethod":[36,0]}}],"vtable":{"id":{"Adt":59},"generics":{"regions":[],"types":[{"Deduplicated":8295},{"Deduplicated":8348}],"const_generics":[],"trait_refs":[]}}},{"def_id":37,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["ops",0]},{"Ident":["function",0]},{"Ident":["FnOnce",0]}],"span":{"data":{"file_id":36,"beg":{"line":242,"col":0},"end":{"line":242,"col":35}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" The version of the call operator that takes a by-value receiver."},{"DocComment":""},{"DocComment":" Instances of `FnOnce` can be called, but might not be callable multiple"},{"DocComment":" times. Because of this, if the only thing known about a type is that it"},{"DocComment":" implements `FnOnce`, it can only be called once."},{"DocComment":""},{"DocComment":" `FnOnce` is implemented automatically by closures that might consume captured"},{"DocComment":" variables, as well as all types that implement [`FnMut`], e.g., (safe)"},{"DocComment":" [function pointers] (since `FnOnce` is a supertrait of [`FnMut`])."},{"DocComment":""},{"DocComment":" Since both [`Fn`] and [`FnMut`] are subtraits of `FnOnce`, any instance of"},{"DocComment":" [`Fn`] or [`FnMut`] can be used where a `FnOnce` is expected."},{"DocComment":""},{"DocComment":" Use `FnOnce` as a bound when you want to accept a parameter of function-like"},{"DocComment":" type and only need to call it once. If you need to call the parameter"},{"DocComment":" repeatedly, use [`FnMut`] as a bound; if you also need it to not mutate"},{"DocComment":" state, use [`Fn`]."},{"DocComment":""},{"DocComment":" See the [chapter on closures in *The Rust Programming Language*][book] for"},{"DocComment":" some more information on this topic."},{"DocComment":""},{"DocComment":" Also of note is the special syntax for `Fn` traits (e.g."},{"DocComment":" `Fn(usize, bool) -> usize`). Those interested in the technical details of"},{"DocComment":" this can refer to [the relevant section in the *Rustonomicon*][nomicon]."},{"DocComment":""},{"DocComment":" [book]: ../../book/ch13-01-closures.html"},{"DocComment":" [function pointers]: fn"},{"DocComment":" [nomicon]: ../../nomicon/hrtb.html"},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" ## Using a `FnOnce` parameter"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" fn consume_with_relish<F>(func: F)"},{"DocComment":" where F: FnOnce() -> String"},{"DocComment":" {"},{"DocComment":" // `func` consumes its captured variables, so it cannot be run more"},{"DocComment":" // than once."},{"DocComment":" println!(\"Consumed: {}\", func());"},{"DocComment":""},{"DocComment":" println!(\"Delicious!\");"},{"DocComment":""},{"DocComment":" // Attempting to invoke `func()` again will throw a `use of moved"},{"DocComment":" // value` error for `func`."},{"DocComment":" }"},{"DocComment":""},{"DocComment":" let x = String::from(\"x\");"},{"DocComment":" let consume_and_return_x = move || x;"},{"DocComment":" consume_with_relish(consume_and_return_x);"},{"DocComment":""},{"DocComment":" // `consume_and_return_x` can no longer be invoked at this point"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"fn_once"},"generics":{"regions":[],"types":[{"index":0,"name":"Self"},{"index":1,"name":"Args"},{"index":2,"name":"Self_Output"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[],"consts":[],"types":[null],"methods":[{"params":{"regions":[],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"call_once","attr_info":{"attributes":[{"DocComment":" Performs the call operation."}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":{"Other":"rust-call"},"inputs":[{"Deduplicated":8294},{"Deduplicated":8295}],"output":{"Deduplicated":8348}},"item":{"id":257,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295},{"Deduplicated":8348}],"const_generics":[],"trait_refs":[{"HashConsedValue":[8403,{"kind":"SelfId","trait_decl_ref":{"regions":[],"skip_binder":{"id":37,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295},{"Deduplicated":8348}],"const_generics":[],"trait_refs":[]}}}}]}]}}},"kind":{"TraitMethod":[37,0]}}],"vtable":{"id":{"Adt":60},"generics":{"regions":[],"types":[{"Deduplicated":8295},{"Deduplicated":8348}],"const_generics":[],"trait_refs":[]}}},{"def_id":38,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["iter",0]},{"Ident":["traits",0]},{"Ident":["collect",0]},{"Ident":["FromIterator",0]}],"span":{"data":{"file_id":32,"beg":{"line":134,"col":0},"end":{"line":134,"col":32}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" Conversion from an [`Iterator`]."},{"DocComment":""},{"DocComment":" By implementing `FromIterator` for a type, you define how it will be"},{"DocComment":" created from an iterator. This is common for types which describe a"},{"DocComment":" collection of some kind."},{"DocComment":""},{"DocComment":" If you want to create a collection from the contents of an iterator, the"},{"DocComment":" [`Iterator::collect()`] method is preferred. However, when you need to"},{"DocComment":" specify the container type, [`FromIterator::from_iter()`] can be more"},{"DocComment":" readable than using a turbofish (e.g. `::<Vec<_>>()`). See the"},{"DocComment":" [`Iterator::collect()`] documentation for more examples of its use."},{"DocComment":""},{"DocComment":" See also: [`IntoIterator`]."},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" Basic usage:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" let five_fives = std::iter::repeat(5).take(5);"},{"DocComment":""},{"DocComment":" let v = Vec::from_iter(five_fives);"},{"DocComment":""},{"DocComment":" assert_eq!(v, vec![5, 5, 5, 5, 5]);"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" Using [`Iterator::collect()`] to implicitly use `FromIterator`:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" let five_fives = std::iter::repeat(5).take(5);"},{"DocComment":""},{"DocComment":" let v: Vec<i32> = five_fives.collect();"},{"DocComment":""},{"DocComment":" assert_eq!(v, vec![5, 5, 5, 5, 5]);"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" Using [`FromIterator::from_iter()`] as a more readable alternative to"},{"DocComment":" [`Iterator::collect()`]:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" use std::collections::VecDeque;"},{"DocComment":" let first = (0..10).collect::<VecDeque<i32>>();"},{"DocComment":" let second = VecDeque::from_iter(0..10);"},{"DocComment":""},{"DocComment":" assert_eq!(first, second);"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" Implementing `FromIterator` for your type:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" // A sample collection, that's just a wrapper over Vec<T>"},{"DocComment":" #[derive(Debug)]"},{"DocComment":" struct MyCollection(Vec<i32>);"},{"DocComment":""},{"DocComment":" // Let's give it some methods so we can create one and add things"},{"DocComment":" // to it."},{"DocComment":" impl MyCollection {"},{"DocComment":" fn new() -> MyCollection {"},{"DocComment":" MyCollection(Vec::new())"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" fn add(&mut self, elem: i32) {"},{"DocComment":" self.0.push(elem);"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" // and we'll implement FromIterator"},{"DocComment":" impl FromIterator<i32> for MyCollection {"},{"DocComment":" fn from_iter<I: IntoIterator<Item=i32>>(iter: I) -> Self {"},{"DocComment":" let mut c = MyCollection::new();"},{"DocComment":""},{"DocComment":" for i in iter {"},{"DocComment":" c.add(i);"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" c"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" // Now we can make a new iterator..."},{"DocComment":" let iter = (0..5).into_iter();"},{"DocComment":""},{"DocComment":" // ... and make a MyCollection out of it"},{"DocComment":" let c = MyCollection::from_iter(iter);"},{"DocComment":""},{"DocComment":" assert_eq!(c.0, vec![0, 1, 2, 3, 4]);"},{"DocComment":""},{"DocComment":" // collect works too!"},{"DocComment":""},{"DocComment":" let iter = (0..5).into_iter();"},{"DocComment":" let c: MyCollection = iter.collect();"},{"DocComment":""},{"DocComment":" assert_eq!(c.0, vec![0, 1, 2, 3, 4]);"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"FromIterator"},"generics":{"regions":[],"types":[{"index":0,"name":"Self"},{"index":1,"name":"A"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[],"consts":[],"types":[],"methods":[{"params":{"regions":[],"types":[{"index":0,"name":"T"},{"index":1,"name":"Clause0_IntoIter"}],"const_generics":[],"trait_clauses":[{"clause_id":0,"span":{"data":{"file_id":32,"beg":{"line":152,"col":20},"end":{"line":152,"col":42}},"generated_from_span":null},"origin":"WhereClauseOnFn","trait_":{"regions":[],"skip_binder":{"id":35,"generics":{"regions":[],"types":[{"Deduplicated":1092},{"Deduplicated":8295},{"HashConsedValue":[1263,{"TypeVar":{"Bound":[1,1]}}]}],"const_generics":[],"trait_refs":[]}}}}],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"from_iter","attr_info":{"attributes":[{"DocComment":" Creates a value from an iterator."},{"DocComment":""},{"DocComment":" See the [module-level documentation] for more."},{"DocComment":""},{"DocComment":" [module-level documentation]: crate::iter"},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" let five_fives = std::iter::repeat(5).take(5);"},{"DocComment":""},{"DocComment":" let v = Vec::from_iter(five_fives);"},{"DocComment":""},{"DocComment":" assert_eq!(v, vec![5, 5, 5, 5, 5]);"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":1091}],"output":{"Deduplicated":8294}},"item":{"id":258,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295},{"Deduplicated":1091},{"Deduplicated":1262}],"const_generics":[],"trait_refs":[{"HashConsedValue":[8404,{"kind":"SelfId","trait_decl_ref":{"regions":[],"skip_binder":{"id":38,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}}}]},{"HashConsedValue":[8405,{"kind":{"Clause":{"Bound":[0,0]}},"trait_decl_ref":{"regions":[],"skip_binder":{"id":35,"generics":{"regions":[],"types":[{"Deduplicated":1092},{"Deduplicated":8295},{"Deduplicated":1263}],"const_generics":[],"trait_refs":[]}}}}]}]}}},"kind":{"TraitMethod":[38,0]}}],"vtable":null},{"def_id":39,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["ops",0]},{"Ident":["try_trait",0]},{"Ident":["Try",0]}],"span":{"data":{"file_id":52,"beg":{"line":133,"col":0},"end":{"line":133,"col":41}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" The `?` operator and `try {}` blocks."},{"DocComment":""},{"DocComment":" `try_*` methods typically involve a type implementing this trait. For"},{"DocComment":" example, the closures passed to [`Iterator::try_fold`] and"},{"DocComment":" [`Iterator::try_for_each`] must return such a type."},{"DocComment":""},{"DocComment":" `Try` types are typically those containing two or more categories of values,"},{"DocComment":" some subset of which are so commonly handled via early returns that it's"},{"DocComment":" worth providing a terse (but still visible) syntax to make that easy."},{"DocComment":""},{"DocComment":" This is most often seen for error handling with [`Result`] and [`Option`]."},{"DocComment":" The quintessential implementation of this trait is on [`ControlFlow`]."},{"DocComment":""},{"DocComment":" # Using `Try` in Generic Code"},{"DocComment":""},{"DocComment":" `Iterator::try_fold` was stabilized to call back in Rust 1.27, but"},{"DocComment":" this trait is much newer. To illustrate the various associated types and"},{"DocComment":" methods, let's implement our own version."},{"DocComment":""},{"DocComment":" As a reminder, an infallible version of a fold looks something like this:"},{"DocComment":" ```"},{"DocComment":" fn simple_fold<A, T>("},{"DocComment":" iter: impl Iterator<Item = T>,"},{"DocComment":" mut accum: A,"},{"DocComment":" mut f: impl FnMut(A, T) -> A,"},{"DocComment":" ) -> A {"},{"DocComment":" for x in iter {"},{"DocComment":" accum = f(accum, x);"},{"DocComment":" }"},{"DocComment":" accum"},{"DocComment":" }"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" So instead of `f` returning just an `A`, we'll need it to return some other"},{"DocComment":" type that produces an `A` in the \"don't short circuit\" path. Conveniently,"},{"DocComment":" that's also the type we need to return from the function."},{"DocComment":""},{"DocComment":" Let's add a new generic parameter `R` for that type, and bound it to the"},{"DocComment":" output type that we want:"},{"DocComment":" ```"},{"DocComment":" # #![feature(try_trait_v2)]"},{"DocComment":" # use std::ops::Try;"},{"DocComment":" fn simple_try_fold_1<A, T, R: Try<Output = A>>("},{"DocComment":" iter: impl Iterator<Item = T>,"},{"DocComment":" mut accum: A,"},{"DocComment":" mut f: impl FnMut(A, T) -> R,"},{"DocComment":" ) -> R {"},{"DocComment":" todo!()"},{"DocComment":" }"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" If we get through the entire iterator, we need to wrap up the accumulator"},{"DocComment":" into the return type using [`Try::from_output`]:"},{"DocComment":" ```"},{"DocComment":" # #![feature(try_trait_v2)]"},{"DocComment":" # use std::ops::{ControlFlow, Try};"},{"DocComment":" fn simple_try_fold_2<A, T, R: Try<Output = A>>("},{"DocComment":" iter: impl Iterator<Item = T>,"},{"DocComment":" mut accum: A,"},{"DocComment":" mut f: impl FnMut(A, T) -> R,"},{"DocComment":" ) -> R {"},{"DocComment":" for x in iter {"},{"DocComment":" let cf = f(accum, x).branch();"},{"DocComment":" match cf {"},{"DocComment":" ControlFlow::Continue(a) => accum = a,"},{"DocComment":" ControlFlow::Break(_) => todo!(),"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":" R::from_output(accum)"},{"DocComment":" }"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" We'll also need [`FromResidual::from_residual`] to turn the residual back"},{"DocComment":" into the original type. But because it's a supertrait of `Try`, we don't"},{"DocComment":" need to mention it in the bounds. All types which implement `Try` can be"},{"DocComment":" recreated from their corresponding residual, so we'll just call it:"},{"DocComment":" ```"},{"DocComment":" # #![feature(try_trait_v2)]"},{"DocComment":" # use std::ops::{ControlFlow, Try};"},{"DocComment":" pub fn simple_try_fold_3<A, T, R: Try<Output = A>>("},{"DocComment":" iter: impl Iterator<Item = T>,"},{"DocComment":" mut accum: A,"},{"DocComment":" mut f: impl FnMut(A, T) -> R,"},{"DocComment":" ) -> R {"},{"DocComment":" for x in iter {"},{"DocComment":" let cf = f(accum, x).branch();"},{"DocComment":" match cf {"},{"DocComment":" ControlFlow::Continue(a) => accum = a,"},{"DocComment":" ControlFlow::Break(r) => return R::from_residual(r),"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":" R::from_output(accum)"},{"DocComment":" }"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" But this \"call `branch`, then `match` on it, and `return` if it was a"},{"DocComment":" `Break`\" is exactly what happens inside the `?` operator. So rather than"},{"DocComment":" do all this manually, we can just use `?` instead:"},{"DocComment":" ```"},{"DocComment":" # #![feature(try_trait_v2)]"},{"DocComment":" # use std::ops::Try;"},{"DocComment":" fn simple_try_fold<A, T, R: Try<Output = A>>("},{"DocComment":" iter: impl Iterator<Item = T>,"},{"DocComment":" mut accum: A,"},{"DocComment":" mut f: impl FnMut(A, T) -> R,"},{"DocComment":" ) -> R {"},{"DocComment":" for x in iter {"},{"DocComment":" accum = f(accum, x)?;"},{"DocComment":" }"},{"DocComment":" R::from_output(accum)"},{"DocComment":" }"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"Try"},"generics":{"regions":[],"types":[{"index":0,"name":"Self"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[{"clause_id":0,"span":{"data":{"file_id":52,"beg":{"line":133,"col":21},"end":{"line":133,"col":41}},"generated_from_span":null},"origin":"WhereClauseOnTrait","trait_":{"regions":[],"skip_binder":{"id":51,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"HashConsedValue":[8407,{"TraitType":[{"HashConsedValue":[8406,{"kind":"SelfId","trait_decl_ref":{"regions":[],"skip_binder":{"id":39,"generics":{"regions":[],"types":[{"Deduplicated":8294}],"const_generics":[],"trait_refs":[]}}}}]},1,{"regions":[],"types":[],"const_generics":[],"trait_refs":[]}]}]}],"const_generics":[],"trait_refs":[]}}}},{"clause_id":1,"span":{"data":{"file_id":52,"beg":{"line":160,"col":19},"end":{"line":160,"col":41}},"generated_from_span":null},"origin":{"TraitItem":1},"trait_":{"regions":[],"skip_binder":{"id":40,"generics":{"regions":[],"types":[{"Deduplicated":8407},{"HashConsedValue":[8408,{"TraitType":[{"Deduplicated":8406},0,{"regions":[],"types":[],"const_generics":[],"trait_refs":[]}]}]},{"HashConsedValue":[8409,{"TraitType":[{"Deduplicated":8406},2,{"regions":[],"types":[],"const_generics":[],"trait_refs":[]}]}]}],"const_generics":[],"trait_refs":[]}}}}],"consts":[],"types":[{"params":{"regions":[],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"Output","attr_info":{"attributes":[{"DocComment":" The type of the value produced by `?` when *not* short-circuiting."}],"inline":null,"rename":null,"public":false},"default":null,"implied_clauses":[]},"kind":{"TraitType":[39,0]}},{"params":{"regions":[],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"Residual","attr_info":{"attributes":[{"DocComment":" The type of the value passed to [`FromResidual::from_residual`]"},{"DocComment":" as part of `?` when short-circuiting."},{"DocComment":""},{"DocComment":" This represents the possible values of the `Self` type which are *not*"},{"DocComment":" represented by the `Output` type."},{"DocComment":""},{"DocComment":" # Note to Implementors"},{"DocComment":""},{"DocComment":" The choice of this type is critical to interconversion."},{"DocComment":" Unlike the `Output` type, which will often be a raw generic type,"},{"DocComment":" this type is typically a newtype of some sort to \"color\" the type"},{"DocComment":" so that it's distinguishable from the residuals of other types."},{"DocComment":""},{"DocComment":" This is why `Result<T, E>::Residual` is not `E`, but `Result<Infallible, E>`."},{"DocComment":" That way it's distinct from `ControlFlow<E>::Residual`, for example,"},{"DocComment":" and thus `?` on `ControlFlow` cannot be used in a method returning `Result`."},{"DocComment":""},{"DocComment":" If you're making a generic type `Foo<T>` that implements `Try<Output = T>`,"},{"DocComment":" then typically you can use `Foo<std::convert::Infallible>` as its `Residual`"},{"DocComment":" type: that type will have a \"hole\" in the correct place, and will maintain the"},{"DocComment":" \"foo-ness\" of the residual so other types need to opt-in to interconversion."}],"inline":null,"rename":null,"public":false},"default":null,"implied_clauses":[]},"kind":{"TraitType":[39,1]}},{"params":{"regions":[],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"Self_Clause1_TryType","attr_info":{"attributes":[],"inline":null,"rename":null,"public":true},"default":null,"implied_clauses":[]},"kind":{"TraitType":[39,2]}}],"methods":[{"params":{"regions":[],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"from_output","attr_info":{"attributes":[{"DocComment":" Constructs the type from its `Output` type."},{"DocComment":""},{"DocComment":" This should be implemented consistently with the `branch` method"},{"DocComment":" such that applying the `?` operator will get back the original value:"},{"DocComment":" `Try::from_output(x).branch() --> ControlFlow::Continue(x)`."},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" #![feature(try_trait_v2)]"},{"DocComment":" use std::ops::Try;"},{"DocComment":""},{"DocComment":" assert_eq!(<Result<_, String> as Try>::from_output(3), Ok(3));"},{"DocComment":" assert_eq!(<Option<_> as Try>::from_output(4), Some(4));"},{"DocComment":" assert_eq!("},{"DocComment":" <std::ops::ControlFlow<String, _> as Try>::from_output(5),"},{"DocComment":" std::ops::ControlFlow::Continue(5),"},{"DocComment":" );"},{"DocComment":""},{"DocComment":" # fn make_question_mark_work() -> Option<()> {"},{"DocComment":" assert_eq!(Option::from_output(4)?, 4);"},{"DocComment":" # None }"},{"DocComment":" # make_question_mark_work();"},{"DocComment":""},{"DocComment":" // This is used, for example, on the accumulator in `try_fold`:"},{"DocComment":" let r = std::iter::empty().try_fold(4, |_, ()| -> Option<_> { unreachable!() });"},{"DocComment":" assert_eq!(r, Some(4));"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8408}],"output":{"Deduplicated":8294}},"item":{"id":259,"generics":{"regions":[],"types":[{"Deduplicated":8294}],"const_generics":[],"trait_refs":[{"Deduplicated":8406}]}}},"kind":{"TraitMethod":[39,0]}},{"params":{"regions":[],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"branch","attr_info":{"attributes":[{"DocComment":" Used in `?` to decide whether the operator should produce a value"},{"DocComment":" (because this returned [`ControlFlow::Continue`])"},{"DocComment":" or propagate a value back to the caller"},{"DocComment":" (because this returned [`ControlFlow::Break`])."},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" #![feature(try_trait_v2)]"},{"DocComment":" use std::ops::{ControlFlow, Try};"},{"DocComment":""},{"DocComment":" assert_eq!(Ok::<_, String>(3).branch(), ControlFlow::Continue(3));"},{"DocComment":" assert_eq!(Err::<String, _>(3).branch(), ControlFlow::Break(Err(3)));"},{"DocComment":""},{"DocComment":" assert_eq!(Some(3).branch(), ControlFlow::Continue(3));"},{"DocComment":" assert_eq!(None::<String>.branch(), ControlFlow::Break(None));"},{"DocComment":""},{"DocComment":" assert_eq!(ControlFlow::<String, _>::Continue(3).branch(), ControlFlow::Continue(3));"},{"DocComment":" assert_eq!("},{"DocComment":" ControlFlow::<_, String>::Break(3).branch(),"},{"DocComment":" ControlFlow::Break(ControlFlow::Break(3)),"},{"DocComment":" );"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8294}],"output":{"HashConsedValue":[8410,{"Adt":{"id":{"Adt":6},"generics":{"regions":[],"types":[{"Deduplicated":8407},{"Deduplicated":8408}],"const_generics":[],"trait_refs":[]}}}]}},"item":{"id":260,"generics":{"regions":[],"types":[{"Deduplicated":8294}],"const_generics":[],"trait_refs":[{"Deduplicated":8406}]}}},"kind":{"TraitMethod":[39,1]}}],"vtable":null},{"def_id":40,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["ops",0]},{"Ident":["try_trait",0]},{"Ident":["Residual",0]}],"span":{"data":{"file_id":52,"beg":{"line":364,"col":0},"end":{"line":364,"col":34}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" Allows retrieving the canonical type implementing [`Try`] that has this type"},{"DocComment":" as its residual and allows it to hold an `O` as its output."},{"DocComment":""},{"DocComment":" If you think of the `Try` trait as splitting a type into its [`Try::Output`]"},{"DocComment":" and [`Try::Residual`] components, this allows putting them back together."},{"DocComment":""},{"DocComment":" For example,"},{"DocComment":" `Result<T, E>: Try<Output = T, Residual = Result<Infallible, E>>`,"},{"DocComment":" and in the other direction,"},{"DocComment":" `<Result<Infallible, E> as Residual<T>>::TryType = Result<T, E>`."}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":null},"generics":{"regions":[],"types":[{"index":0,"name":"Self"},{"index":1,"name":"O"},{"index":2,"name":"Self_TryType"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[{"regions":[],"skip_binder":{"trait_ref":{"HashConsedValue":[8412,{"kind":{"ParentClause":[{"HashConsedValue":[8411,{"kind":"SelfId","trait_decl_ref":{"regions":[],"skip_binder":{"id":40,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295},{"Deduplicated":8348}],"const_generics":[],"trait_refs":[]}}}}]},0]},"trait_decl_ref":{"regions":[],"skip_binder":{"id":39,"generics":{"regions":[],"types":[{"Deduplicated":8348}],"const_generics":[],"trait_refs":[]}}}}]},"type_id":0,"ty":{"Deduplicated":8295}}},{"regions":[],"skip_binder":{"trait_ref":{"Deduplicated":8412},"type_id":1,"ty":{"Deduplicated":8294}}}]},"implied_clauses":[{"clause_id":0,"span":{"data":{"file_id":52,"beg":{"line":368,"col":18},"end":{"line":368,"col":58}},"generated_from_span":null},"origin":{"TraitItem":0},"trait_":{"regions":[],"skip_binder":{"id":39,"generics":{"regions":[],"types":[{"Deduplicated":8348}],"const_generics":[],"trait_refs":[]}}}}],"consts":[],"types":[null],"methods":[],"vtable":null},{"def_id":41,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["iter",0]},{"Ident":["traits",0]},{"Ident":["collect",0]},{"Ident":["Extend",0]}],"span":{"data":{"file_id":32,"beg":{"line":397,"col":0},"end":{"line":397,"col":19}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" Extend a collection with the contents of an iterator."},{"DocComment":""},{"DocComment":" Iterators produce a series of values, and collections can also be thought"},{"DocComment":" of as a series of values. The `Extend` trait bridges this gap, allowing you"},{"DocComment":" to extend a collection by including the contents of that iterator. When"},{"DocComment":" extending a collection with an already existing key, that entry is updated"},{"DocComment":" or, in the case of collections that permit multiple entries with equal"},{"DocComment":" keys, that entry is inserted."},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" Basic usage:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" // You can extend a String with some chars:"},{"DocComment":" let mut message = String::from(\"The first three letters are: \");"},{"DocComment":""},{"DocComment":" message.extend(&['a', 'b', 'c']);"},{"DocComment":""},{"DocComment":" assert_eq!(\"abc\", &message[29..32]);"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" Implementing `Extend`:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" // A sample collection, that's just a wrapper over Vec<T>"},{"DocComment":" #[derive(Debug)]"},{"DocComment":" struct MyCollection(Vec<i32>);"},{"DocComment":""},{"DocComment":" // Let's give it some methods so we can create one and add things"},{"DocComment":" // to it."},{"DocComment":" impl MyCollection {"},{"DocComment":" fn new() -> MyCollection {"},{"DocComment":" MyCollection(Vec::new())"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" fn add(&mut self, elem: i32) {"},{"DocComment":" self.0.push(elem);"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" // since MyCollection has a list of i32s, we implement Extend for i32"},{"DocComment":" impl Extend<i32> for MyCollection {"},{"DocComment":""},{"DocComment":" // This is a bit simpler with the concrete type signature: we can call"},{"DocComment":" // extend on anything which can be turned into an Iterator which gives"},{"DocComment":" // us i32s. Because we need i32s to put into MyCollection."},{"DocComment":" fn extend<T: IntoIterator<Item=i32>>(&mut self, iter: T) {"},{"DocComment":""},{"DocComment":" // The implementation is very straightforward: loop through the"},{"DocComment":" // iterator, and add() each element to ourselves."},{"DocComment":" for elem in iter {"},{"DocComment":" self.add(elem);"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" let mut c = MyCollection::new();"},{"DocComment":""},{"DocComment":" c.add(5);"},{"DocComment":" c.add(6);"},{"DocComment":" c.add(7);"},{"DocComment":""},{"DocComment":" // let's extend our collection with three more numbers"},{"DocComment":" c.extend(vec![1, 2, 3]);"},{"DocComment":""},{"DocComment":" // we've added these elements onto the end"},{"DocComment":" assert_eq!(\"MyCollection([5, 6, 7, 1, 2, 3])\", format!(\"{c:?}\"));"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":null},"generics":{"regions":[],"types":[{"index":0,"name":"Self"},{"index":1,"name":"A"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[],"consts":[],"types":[],"methods":[{"params":{"regions":[{"index":0,"name":null,"mutability":"Unknown"}],"types":[{"index":0,"name":"T"},{"index":1,"name":"Clause0_IntoIter"}],"const_generics":[],"trait_clauses":[{"clause_id":0,"span":{"data":{"file_id":32,"beg":{"line":416,"col":17},"end":{"line":416,"col":39}},"generated_from_span":null},"origin":"WhereClauseOnFn","trait_":{"regions":[],"skip_binder":{"id":35,"generics":{"regions":[],"types":[{"Deduplicated":1092},{"Deduplicated":8295},{"Deduplicated":1263}],"const_generics":[],"trait_refs":[]}}}}],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"extend","attr_info":{"attributes":[{"DocComment":" Extends a collection with the contents of an iterator."},{"DocComment":""},{"DocComment":" As this is the only required method for this trait, the [trait-level] docs"},{"DocComment":" contain more details."},{"DocComment":""},{"DocComment":" [trait-level]: Extend"},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" // You can extend a String with some chars:"},{"DocComment":" let mut message = String::from(\"abc\");"},{"DocComment":""},{"DocComment":" message.extend(['d', 'e', 'f'].iter());"},{"DocComment":""},{"DocComment":" assert_eq!(\"abcdef\", &message);"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8363},{"Deduplicated":1091}],"output":{"Deduplicated":1108}},"item":{"id":261,"generics":{"regions":[{"Var":{"Bound":[0,0]}}],"types":[{"Deduplicated":8294},{"Deduplicated":8295},{"Deduplicated":1091},{"Deduplicated":1262}],"const_generics":[],"trait_refs":[{"HashConsedValue":[8413,{"kind":"SelfId","trait_decl_ref":{"regions":[],"skip_binder":{"id":41,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}}}]},{"Deduplicated":8405}]}}},"kind":{"TraitMethod":[41,0]}},null,null,null],"vtable":null},{"def_id":42,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["iter",0]},{"Ident":["traits",0]},{"Ident":["double_ended",0]},{"Ident":["DoubleEndedIterator",0]}],"span":{"data":{"file_id":53,"beg":{"line":43,"col":0},"end":{"line":43,"col":53}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" An iterator able to yield elements from both ends."},{"DocComment":""},{"DocComment":" Something that implements `DoubleEndedIterator` has one extra capability"},{"DocComment":" over something that implements [`Iterator`]: the ability to also take"},{"DocComment":" `Item`s from the back, as well as the front."},{"DocComment":""},{"DocComment":" It is important to note that both back and forth work on the same range,"},{"DocComment":" and do not cross: iteration is over when they meet in the middle."},{"DocComment":""},{"DocComment":" In a similar fashion to the [`Iterator`] protocol, once a"},{"DocComment":" `DoubleEndedIterator` returns [`None`] from a [`next_back()`], calling it"},{"DocComment":" again may or may not ever return [`Some`] again. [`next()`] and"},{"DocComment":" [`next_back()`] are interchangeable for this purpose."},{"DocComment":""},{"DocComment":" [`next_back()`]: DoubleEndedIterator::next_back"},{"DocComment":" [`next()`]: Iterator::next"},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" Basic usage:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" let numbers = vec![1, 2, 3, 4, 5, 6];"},{"DocComment":""},{"DocComment":" let mut iter = numbers.iter();"},{"DocComment":""},{"DocComment":" assert_eq!(Some(&1), iter.next());"},{"DocComment":" assert_eq!(Some(&6), iter.next_back());"},{"DocComment":" assert_eq!(Some(&5), iter.next_back());"},{"DocComment":" assert_eq!(Some(&2), iter.next());"},{"DocComment":" assert_eq!(Some(&3), iter.next());"},{"DocComment":" assert_eq!(Some(&4), iter.next());"},{"DocComment":" assert_eq!(None, iter.next());"},{"DocComment":" assert_eq!(None, iter.next_back());"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"DoubleEndedIterator"},"generics":{"regions":[],"types":[{"index":0,"name":"Self"},{"index":1,"name":"Self_Clause0_Item"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[{"clause_id":0,"span":{"data":{"file_id":53,"beg":{"line":43,"col":37},"end":{"line":43,"col":53}},"generated_from_span":null},"origin":"WhereClauseOnTrait","trait_":{"regions":[],"skip_binder":{"id":21,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}}}],"consts":[],"types":[],"methods":[{"params":{"regions":[{"index":0,"name":null,"mutability":"Unknown"}],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"next_back","attr_info":{"attributes":[{"DocComment":" Removes and returns an element from the end of the iterator."},{"DocComment":""},{"DocComment":" Returns `None` when there are no more elements."},{"DocComment":""},{"DocComment":" The [trait-level] docs contain more details."},{"DocComment":""},{"DocComment":" [trait-level]: DoubleEndedIterator"},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" Basic usage:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" let numbers = vec![1, 2, 3, 4, 5, 6];"},{"DocComment":""},{"DocComment":" let mut iter = numbers.iter();"},{"DocComment":""},{"DocComment":" assert_eq!(Some(&1), iter.next());"},{"DocComment":" assert_eq!(Some(&6), iter.next_back());"},{"DocComment":" assert_eq!(Some(&5), iter.next_back());"},{"DocComment":" assert_eq!(Some(&2), iter.next());"},{"DocComment":" assert_eq!(Some(&3), iter.next());"},{"DocComment":" assert_eq!(Some(&4), iter.next());"},{"DocComment":" assert_eq!(None, iter.next());"},{"DocComment":" assert_eq!(None, iter.next_back());"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" # Remarks"},{"DocComment":""},{"DocComment":" The elements yielded by `DoubleEndedIterator`'s methods may differ from"},{"DocComment":" the ones yielded by [`Iterator`]'s methods:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" let vec = vec![(1, 'a'), (1, 'b'), (1, 'c'), (2, 'a'), (2, 'b')];"},{"DocComment":" let uniq_by_fst_comp = || {"},{"DocComment":" let mut seen = std::collections::HashSet::new();"},{"DocComment":" vec.iter().copied().filter(move |x| seen.insert(x.0))"},{"DocComment":" };"},{"DocComment":""},{"DocComment":" assert_eq!(uniq_by_fst_comp().last(), Some((2, 'a')));"},{"DocComment":" assert_eq!(uniq_by_fst_comp().next_back(), Some((2, 'b')));"},{"DocComment":""},{"DocComment":" assert_eq!("},{"DocComment":" uniq_by_fst_comp().fold(vec![], |mut v, x| {v.push(x); v}),"},{"DocComment":" vec![(1, 'a'), (2, 'a')]"},{"DocComment":" );"},{"DocComment":" assert_eq!("},{"DocComment":" uniq_by_fst_comp().rfold(vec![], |mut v, x| {v.push(x); v}),"},{"DocComment":" vec![(2, 'b'), (1, 'c')]"},{"DocComment":" );"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8363}],"output":{"Deduplicated":8385}},"item":{"id":265,"generics":{"regions":[{"Var":{"Bound":[0,0]}}],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[{"HashConsedValue":[8414,{"kind":"SelfId","trait_decl_ref":{"regions":[],"skip_binder":{"id":42,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}}}]}]}}},"kind":{"TraitMethod":[42,0]}},null,null,null,null,null],"vtable":{"id":{"Adt":61},"generics":{"regions":[],"types":[{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}},{"def_id":43,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["iter",0]},{"Ident":["traits",0]},{"Ident":["exact_size",0]},{"Ident":["ExactSizeIterator",0]}],"span":{"data":{"file_id":54,"beg":{"line":86,"col":0},"end":{"line":86,"col":37}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" An iterator that knows its exact length."},{"DocComment":""},{"DocComment":" Many [`Iterator`]s don't know how many times they will iterate, but some do."},{"DocComment":" If an iterator knows how many times it can iterate, providing access to"},{"DocComment":" that information can be useful. For example, if you want to iterate"},{"DocComment":" backwards, a good start is to know where the end is."},{"DocComment":""},{"DocComment":" When implementing an `ExactSizeIterator`, you must also implement"},{"DocComment":" [`Iterator`]. When doing so, the implementation of [`Iterator::size_hint`]"},{"DocComment":" *must* return the exact size of the iterator."},{"DocComment":""},{"DocComment":" The [`len`] method has a default implementation, so you usually shouldn't"},{"DocComment":" implement it. However, you may be able to provide a more performant"},{"DocComment":" implementation than the default, so overriding it in this case makes sense."},{"DocComment":""},{"DocComment":" Note that this trait is a safe trait and as such does *not* and *cannot*"},{"DocComment":" guarantee that the returned length is correct. This means that `unsafe`"},{"DocComment":" code **must not** rely on the correctness of [`Iterator::size_hint`]. The"},{"DocComment":" unstable and unsafe [`TrustedLen`](super::marker::TrustedLen) trait gives"},{"DocComment":" this additional guarantee."},{"DocComment":""},{"DocComment":" [`len`]: ExactSizeIterator::len"},{"DocComment":""},{"DocComment":" # When *shouldn't* an adapter be `ExactSizeIterator`?"},{"DocComment":""},{"DocComment":" If an adapter makes an iterator *longer*, then it's usually incorrect for"},{"DocComment":" that adapter to implement `ExactSizeIterator`. The inner exact-sized"},{"DocComment":" iterator might already be `usize::MAX`-long, and thus the length of the"},{"DocComment":" longer adapted iterator would no longer be exactly representable in `usize`."},{"DocComment":""},{"DocComment":" This is why [`Chain<A, B>`](crate::iter::Chain) isn't `ExactSizeIterator`,"},{"DocComment":" even when `A` and `B` are both `ExactSizeIterator`."},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" Basic usage:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" // a finite range knows exactly how many times it will iterate"},{"DocComment":" let five = 0..5;"},{"DocComment":""},{"DocComment":" assert_eq!(5, five.len());"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" In the [module-level docs], we implemented an [`Iterator`], `Counter`."},{"DocComment":" Let's implement `ExactSizeIterator` for it as well:"},{"DocComment":""},{"DocComment":" [module-level docs]: crate::iter"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" # struct Counter {"},{"DocComment":" # count: usize,"},{"DocComment":" # }"},{"DocComment":" # impl Counter {"},{"DocComment":" # fn new() -> Counter {"},{"DocComment":" # Counter { count: 0 }"},{"DocComment":" # }"},{"DocComment":" # }"},{"DocComment":" # impl Iterator for Counter {"},{"DocComment":" # type Item = usize;"},{"DocComment":" # fn next(&mut self) -> Option<Self::Item> {"},{"DocComment":" # self.count += 1;"},{"DocComment":" # if self.count < 6 {"},{"DocComment":" # Some(self.count)"},{"DocComment":" # } else {"},{"DocComment":" # None"},{"DocComment":" # }"},{"DocComment":" # }"},{"DocComment":" # }"},{"DocComment":" impl ExactSizeIterator for Counter {"},{"DocComment":" // We can easily calculate the remaining number of iterations."},{"DocComment":" fn len(&self) -> usize {"},{"DocComment":" 5 - self.count"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" // And now we can use it!"},{"DocComment":""},{"DocComment":" let mut counter = Counter::new();"},{"DocComment":""},{"DocComment":" assert_eq!(5, counter.len());"},{"DocComment":" let _ = counter.next();"},{"DocComment":" assert_eq!(4, counter.len());"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":null},"generics":{"regions":[],"types":[{"index":0,"name":"Self"},{"index":1,"name":"Self_Clause0_Item"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[{"clause_id":0,"span":{"data":{"file_id":54,"beg":{"line":86,"col":29},"end":{"line":86,"col":37}},"generated_from_span":null},"origin":"WhereClauseOnTrait","trait_":{"regions":[],"skip_binder":{"id":21,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}}}],"consts":[],"types":[],"methods":[null,null],"vtable":{"id":{"Adt":62},"generics":{"regions":[],"types":[{"Deduplicated":8295}],"const_generics":[],"trait_refs":[]}}},{"def_id":44,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["iter",0]},{"Ident":["adapters",0]},{"Ident":["zip",0]},{"Ident":["TrustedRandomAccessNoCoerce",0]}],"span":{"data":{"file_id":34,"beg":{"line":576,"col":0},"end":{"line":576,"col":51}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" Like [`TrustedRandomAccess`] but without any of the requirements / guarantees around"},{"DocComment":" coercions to supertypes after `__iterator_get_unchecked` (they aren’t allowed here!), and"},{"DocComment":" without the requirement that subtypes / supertypes implement `TrustedRandomAccessNoCoerce`."},{"DocComment":""},{"DocComment":" This trait was created in PR #85874 to fix soundness issue #85873 without performance regressions."},{"DocComment":" It is subject to change as we might want to build a more generally useful (for performance"},{"DocComment":" optimizations) and more sophisticated trait or trait hierarchy that replaces or extends"},{"DocComment":" [`TrustedRandomAccess`] and `TrustedRandomAccessNoCoerce`."}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":null},"generics":{"regions":[],"types":[{"index":0,"name":"Self"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[],"consts":[{"name":"MAY_HAVE_SIDE_EFFECT","attr_info":{"attributes":[{"DocComment":" `true` if getting an iterator element may have side effects."},{"DocComment":" Remember to take inner iterators into account."}],"inline":null,"rename":null,"public":true},"ty":{"Deduplicated":1225},"default":null}],"types":[],"methods":[null],"vtable":null},{"def_id":45,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["ops",0]},{"Ident":["index",0]},{"Ident":["Index",0]}],"span":{"data":{"file_id":64,"beg":{"line":59,"col":0},"end":{"line":59,"col":34}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" Used for indexing operations (`container[index]`) in immutable contexts."},{"DocComment":""},{"DocComment":" `container[index]` is actually syntactic sugar for `*container.index(index)`,"},{"DocComment":" but only when used as an immutable value. If a mutable value is requested,"},{"DocComment":" [`IndexMut`] is used instead. This allows nice things such as"},{"DocComment":" `let value = v[index]` if the type of `value` implements [`Copy`]."},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" The following example implements `Index` on a read-only `NucleotideCount`"},{"DocComment":" container, enabling individual counts to be retrieved with index syntax."},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" use std::ops::Index;"},{"DocComment":""},{"DocComment":" enum Nucleotide {"},{"DocComment":" A,"},{"DocComment":" C,"},{"DocComment":" G,"},{"DocComment":" T,"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" struct NucleotideCount {"},{"DocComment":" a: usize,"},{"DocComment":" c: usize,"},{"DocComment":" g: usize,"},{"DocComment":" t: usize,"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl Index<Nucleotide> for NucleotideCount {"},{"DocComment":" type Output = usize;"},{"DocComment":""},{"DocComment":" fn index(&self, nucleotide: Nucleotide) -> &Self::Output {"},{"DocComment":" match nucleotide {"},{"DocComment":" Nucleotide::A => &self.a,"},{"DocComment":" Nucleotide::C => &self.c,"},{"DocComment":" Nucleotide::G => &self.g,"},{"DocComment":" Nucleotide::T => &self.t,"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" let nucleotide_count = NucleotideCount {a: 14, c: 9, g: 10, t: 12};"},{"DocComment":" assert_eq!(nucleotide_count[Nucleotide::A], 14);"},{"DocComment":" assert_eq!(nucleotide_count[Nucleotide::C], 9);"},{"DocComment":" assert_eq!(nucleotide_count[Nucleotide::G], 10);"},{"DocComment":" assert_eq!(nucleotide_count[Nucleotide::T], 12);"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"index"},"generics":{"regions":[],"types":[{"index":0,"name":"Self"},{"index":1,"name":"Idx"},{"index":2,"name":"Self_Output"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[],"consts":[],"types":[null],"methods":[{"params":{"regions":[{"index":0,"name":null,"mutability":"Unknown"}],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"index","attr_info":{"attributes":[{"DocComment":" Performs the indexing (`container[index]`) operation."},{"DocComment":""},{"DocComment":" # Panics"},{"DocComment":""},{"DocComment":" May panic if the index is out of 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A helper trait used for indexing operations."},{"DocComment":""},{"DocComment":" Implementations of this trait have to promise that if the argument"},{"DocComment":" to `get_unchecked(_mut)` is a safe reference, then so is the 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performing any bounds checking."},{"DocComment":""},{"DocComment":" Calling this method with an out-of-bounds index or a dangling `slice` pointer"},{"DocComment":" is *[undefined behavior]* even if the resulting pointer is not used."},{"DocComment":""},{"DocComment":" [undefined behavior]: https://doc.rust-lang.org/reference/behavior-considered-undefined.html"}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":true,"abi":"Rust","inputs":[{"Deduplicated":8294},{"Deduplicated":8421}],"output":{"Deduplicated":8422}},"item":{"id":287,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295},{"Deduplicated":8348}],"const_generics":[],"trait_refs":[{"Deduplicated":8418}]}}},"kind":{"TraitMethod":[46,2]}},{"params":{"regions":[],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"get_unchecked_mut","attr_info":{"attributes":[{"DocComment":" Returns a mutable pointer 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https://doc.rust-lang.org/reference/behavior-considered-undefined.html"}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":true,"abi":"Rust","inputs":[{"Deduplicated":8294},{"Deduplicated":8423}],"output":{"Deduplicated":8424}},"item":{"id":288,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295},{"Deduplicated":8348}],"const_generics":[],"trait_refs":[{"Deduplicated":8418}]}}},"kind":{"TraitMethod":[46,3]}},{"params":{"regions":[{"index":0,"name":null,"mutability":"Unknown"}],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"index","attr_info":{"attributes":[{"DocComment":" Returns a shared reference to the output at this location, panicking"},{"DocComment":" if out of 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It is the reciprocal of [`TryInto`]."},{"DocComment":""},{"DocComment":" This is useful when you are doing a type conversion that may"},{"DocComment":" trivially succeed but may also need special handling."},{"DocComment":" For example, there is no way to convert an [`i64`] into an [`i32`]"},{"DocComment":" using the [`From`] trait, because an [`i64`] may contain a value"},{"DocComment":" that an [`i32`] cannot represent and so the conversion would lose data."},{"DocComment":" This might be handled by truncating the [`i64`] to an [`i32`] or by"},{"DocComment":" simply returning [`i32::MAX`], or by some other method. The [`From`]"},{"DocComment":" trait is intended for perfect conversions, so the `TryFrom` trait"},{"DocComment":" informs the programmer when a type conversion could go bad and lets"},{"DocComment":" them decide how to handle it."},{"DocComment":""},{"DocComment":" # Generic Implementations"},{"DocComment":""},{"DocComment":" - `TryFrom<T> for U` implies [`TryInto`]`<U> for T`"},{"DocComment":" - [`try_from`] is reflexive, which means that `TryFrom<T> for T`"},{"DocComment":" is implemented and cannot fail -- the associated `Error` type for"},{"DocComment":" calling `T::try_from()` on a value of type `T` is [`Infallible`]."},{"DocComment":" When the [`!`] type is stabilized [`Infallible`] and [`!`] will be"},{"DocComment":" equivalent."},{"DocComment":""},{"DocComment":" Prefer using [`TryInto`] over [`TryFrom`] when specifying trait bounds on a generic function"},{"DocComment":" to ensure that types that only implement [`TryInto`] can be used as well."},{"DocComment":""},{"DocComment":" `TryFrom<T>` can be implemented as follows:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" struct GreaterThanZero(i32);"},{"DocComment":""},{"DocComment":" impl TryFrom<i32> for GreaterThanZero {"},{"DocComment":" type Error = &'static str;"},{"DocComment":""},{"DocComment":" fn try_from(value: i32) -> Result<Self, Self::Error> {"},{"DocComment":" if value <= 0 {"},{"DocComment":" Err(\"GreaterThanZero only accepts values greater than zero!\")"},{"DocComment":" } else {"},{"DocComment":" Ok(GreaterThanZero(value))"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" As described, [`i32`] implements `TryFrom<`[`i64`]`>`:"},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" let big_number = 1_000_000_000_000i64;"},{"DocComment":" // Silently truncates `big_number`, requires detecting"},{"DocComment":" // and handling the truncation after the fact."},{"DocComment":" let smaller_number = big_number as i32;"},{"DocComment":" assert_eq!(smaller_number, -727379968);"},{"DocComment":""},{"DocComment":" // Returns an error because `big_number` is too big to"},{"DocComment":" // fit in an `i32`."},{"DocComment":" let try_smaller_number = i32::try_from(big_number);"},{"DocComment":" assert!(try_smaller_number.is_err());"},{"DocComment":""},{"DocComment":" // Returns `Ok(3)`."},{"DocComment":" let try_successful_smaller_number = i32::try_from(3);"},{"DocComment":" assert!(try_successful_smaller_number.is_ok());"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" [`try_from`]: TryFrom::try_from"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"TryFrom"},"generics":{"regions":[],"types":[{"index":0,"name":"Self"},{"index":1,"name":"T"},{"index":2,"name":"Self_Error"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[],"consts":[],"types":[null],"methods":[{"params":{"regions":[],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"try_from","attr_info":{"attributes":[{"DocComment":" Performs the conversion."}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8295}],"output":{"Deduplicated":8425}},"item":{"id":297,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295},{"Deduplicated":8348}],"const_generics":[],"trait_refs":[{"HashConsedValue":[8426,{"kind":"SelfId","trait_decl_ref":{"regions":[],"skip_binder":{"id":47,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295},{"Deduplicated":8348}],"const_generics":[],"trait_refs":[]}}}}]}]}}},"kind":{"TraitMethod":[47,0]}}],"vtable":null},{"def_id":48,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["ops",0]},{"Ident":["index",0]},{"Ident":["IndexMut",0]}],"span":{"data":{"file_id":64,"beg":{"line":170,"col":0},"end":{"line":170,"col":57}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" Used for indexing operations (`container[index]`) in mutable contexts."},{"DocComment":""},{"DocComment":" `container[index]` is actually syntactic sugar for"},{"DocComment":" `*container.index_mut(index)`, but only when used as a mutable value. If"},{"DocComment":" an immutable value is requested, the [`Index`] trait is used instead. This"},{"DocComment":" allows nice things such as `v[index] = value`."},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" A very simple implementation of a `Balance` struct that has two sides, where"},{"DocComment":" each can be indexed mutably and immutably."},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" use std::ops::{Index, IndexMut};"},{"DocComment":""},{"DocComment":" #[derive(Debug)]"},{"DocComment":" enum Side {"},{"DocComment":" Left,"},{"DocComment":" Right,"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" #[derive(Debug, PartialEq)]"},{"DocComment":" enum Weight {"},{"DocComment":" Kilogram(f32),"},{"DocComment":" Pound(f32),"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" struct Balance {"},{"DocComment":" pub left: Weight,"},{"DocComment":" pub right: Weight,"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl Index<Side> for Balance {"},{"DocComment":" type Output = Weight;"},{"DocComment":""},{"DocComment":" fn index(&self, index: Side) -> &Self::Output {"},{"DocComment":" println!(\"Accessing {index:?}-side of balance immutably\");"},{"DocComment":" match index {"},{"DocComment":" Side::Left => &self.left,"},{"DocComment":" Side::Right => &self.right,"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" impl IndexMut<Side> for Balance {"},{"DocComment":" fn index_mut(&mut self, index: Side) -> &mut Self::Output {"},{"DocComment":" println!(\"Accessing {index:?}-side of balance mutably\");"},{"DocComment":" match index {"},{"DocComment":" Side::Left => &mut self.left,"},{"DocComment":" Side::Right => &mut self.right,"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" let mut balance = Balance {"},{"DocComment":" right: Weight::Kilogram(2.5),"},{"DocComment":" left: Weight::Pound(1.5),"},{"DocComment":" };"},{"DocComment":""},{"DocComment":" // In this case, `balance[Side::Right]` is sugar for"},{"DocComment":" // `*balance.index(Side::Right)`, since we are only *reading*"},{"DocComment":" // `balance[Side::Right]`, not writing it."},{"DocComment":" assert_eq!(balance[Side::Right], Weight::Kilogram(2.5));"},{"DocComment":""},{"DocComment":" // However, in this case `balance[Side::Left]` is sugar for"},{"DocComment":" // `*balance.index_mut(Side::Left)`, since we are writing"},{"DocComment":" // `balance[Side::Left]`."},{"DocComment":" balance[Side::Left] = Weight::Kilogram(3.0);"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"index_mut"},"generics":{"regions":[],"types":[{"index":0,"name":"Self"},{"index":1,"name":"Idx"},{"index":2,"name":"Self_Clause0_Output"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[{"clause_id":0,"span":{"data":{"file_id":64,"beg":{"line":170,"col":39},"end":{"line":170,"col":57}},"generated_from_span":null},"origin":"WhereClauseOnTrait","trait_":{"regions":[],"skip_binder":{"id":45,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295},{"Deduplicated":8348}],"const_generics":[],"trait_refs":[]}}}}],"consts":[],"types":[],"methods":[{"params":{"regions":[{"index":0,"name":null,"mutability":"Unknown"}],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"index_mut","attr_info":{"attributes":[{"DocComment":" Performs the mutable indexing (`container[index]`) operation."},{"DocComment":""},{"DocComment":" # Panics"},{"DocComment":""},{"DocComment":" May panic if the index is out of bounds."}],"inline":null,"rename":null,"public":true},"signature":{"is_unsafe":false,"abi":"Rust","inputs":[{"Deduplicated":8363},{"Deduplicated":8295}],"output":{"Deduplicated":8419}},"item":{"id":301,"generics":{"regions":[{"Var":{"Bound":[0,0]}}],"types":[{"Deduplicated":8294},{"Deduplicated":8295},{"Deduplicated":8348}],"const_generics":[],"trait_refs":[{"HashConsedValue":[8427,{"kind":"SelfId","trait_decl_ref":{"regions":[],"skip_binder":{"id":48,"generics":{"regions":[],"types":[{"Deduplicated":8294},{"Deduplicated":8295},{"Deduplicated":8348}],"const_generics":[],"trait_refs":[]}}}}]}]}}},"kind":{"TraitMethod":[48,0]}}],"vtable":{"id":{"Adt":65},"generics":{"regions":[],"types":[{"Deduplicated":8295},{"Deduplicated":8348}],"const_generics":[],"trait_refs":[]}}},{"def_id":49,"item_meta":{"name":[{"Ident":["core",0]},{"Ident":["ops",0]},{"Ident":["bit",0]},{"Ident":["BitAnd",0]}],"span":{"data":{"file_id":66,"beg":{"line":150,"col":0},"end":{"line":150,"col":34}},"generated_from_span":null},"source_text":null,"attr_info":{"attributes":[{"DocComment":" The bitwise AND operator `&`."},{"DocComment":""},{"DocComment":" Note that `Rhs` is `Self` by default, but this is not mandatory."},{"DocComment":""},{"DocComment":" # Examples"},{"DocComment":""},{"DocComment":" An implementation of `BitAnd` for a wrapper around `bool`."},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" use std::ops::BitAnd;"},{"DocComment":""},{"DocComment":" #[derive(Debug, PartialEq)]"},{"DocComment":" struct Scalar(bool);"},{"DocComment":""},{"DocComment":" impl BitAnd for Scalar {"},{"DocComment":" type Output = Self;"},{"DocComment":""},{"DocComment":" // rhs is the \"right-hand side\" of the expression `a & b`"},{"DocComment":" fn bitand(self, rhs: Self) -> Self::Output {"},{"DocComment":" Self(self.0 & rhs.0)"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" assert_eq!(Scalar(true) & Scalar(true), Scalar(true));"},{"DocComment":" assert_eq!(Scalar(true) & Scalar(false), Scalar(false));"},{"DocComment":" assert_eq!(Scalar(false) & Scalar(true), Scalar(false));"},{"DocComment":" assert_eq!(Scalar(false) & Scalar(false), Scalar(false));"},{"DocComment":" ```"},{"DocComment":""},{"DocComment":" An implementation of `BitAnd` for a wrapper around `Vec<bool>`."},{"DocComment":""},{"DocComment":" ```"},{"DocComment":" use std::ops::BitAnd;"},{"DocComment":""},{"DocComment":" #[derive(Debug, PartialEq)]"},{"DocComment":" struct BooleanVector(Vec<bool>);"},{"DocComment":""},{"DocComment":" impl BitAnd for BooleanVector {"},{"DocComment":" type Output = Self;"},{"DocComment":""},{"DocComment":" fn bitand(self, Self(rhs): Self) -> Self::Output {"},{"DocComment":" let Self(lhs) = self;"},{"DocComment":" assert_eq!(lhs.len(), rhs.len());"},{"DocComment":" Self("},{"DocComment":" lhs.iter()"},{"DocComment":" .zip(rhs.iter())"},{"DocComment":" .map(|(x, y)| *x & *y)"},{"DocComment":" .collect()"},{"DocComment":" )"},{"DocComment":" }"},{"DocComment":" }"},{"DocComment":""},{"DocComment":" let bv1 = BooleanVector(vec![true, true, false, false]);"},{"DocComment":" let bv2 = BooleanVector(vec![true, false, true, false]);"},{"DocComment":" let expected = BooleanVector(vec![true, false, false, false]);"},{"DocComment":" assert_eq!(bv1 & bv2, expected);"},{"DocComment":" ```"}],"inline":null,"rename":null,"public":true},"is_local":false,"opacity":"Foreign","lang_item":"bitand"},"generics":{"regions":[],"types":[{"index":0,"name":"Self"},{"index":1,"name":"Rhs"},{"index":2,"name":"Self_Output"}],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"implied_clauses":[],"consts":[],"types":[null],"methods":[{"params":{"regions":[],"types":[],"const_generics":[],"trait_clauses":[],"regions_outlive":[],"types_outlive":[],"trait_type_constraints":[]},"skip_binder":{"name":"bitand","attr_info":{"attributes":[{"DocComment":" Performs the `&` operation."},{"DocComment":""},{"DocComment":" # 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For more information on this, see the"},{"DocComment":" documentation for [`Into`]."},{"DocComment":""},{"DocComment":" Prefer using [`TryInto`] over [`TryFrom`] when specifying trait bounds on a generic function"},{"DocComment":" to ensure that types that only implement [`TryInto`] can be used as well."},{"DocComment":""},{"DocComment":" # Implementing `TryInto`"},{"DocComment":""},{"DocComment":" This suffers the same restrictions and reasoning as implementing"},{"DocComment":" [`Into`], see there for 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ff::PrimeField for Fp {\n type Repr = [u8; 32];\n\n const MODULUS: &'static str =\n \"0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001\";\n const TWO_INV: Self = Fp::from_raw([\n 0xcc96987680000001,\n 0x11234c7e04a67c8d,\n 0x0000000000000000,\n 0x2000000000000000,\n ]);\n const NUM_BITS: u32 = 255;\n const CAPACITY: u32 = 254;\n const MULTIPLICATIVE_GENERATOR: Self = GENERATOR;\n const S: u32 = S;\n const ROOT_OF_UNITY: Self = ROOT_OF_UNITY;\n const ROOT_OF_UNITY_INV: Self = Fp::from_raw([\n 0xf0b87c7db2ce91f6,\n 0x84a0a1d8859f066f,\n 0xb4ed8e647196dad1,\n 0x2cd5282c53116b5c,\n ]);\n const DELTA: Self = DELTA;\n\n fn from_u128(v: u128) -> Self {\n Fp::from_raw([v as u64, (v >> 64) as u64, 0, 0])\n }\n\n fn from_repr(repr: Self::Repr) -> CtOption<Self> {\n let mut tmp = Fp([0, 0, 0, 0]);\n\n tmp.0[0] = u64::from_le_bytes(repr[0..8].try_into().unwrap());\n tmp.0[1] = u64::from_le_bytes(repr[8..16].try_into().unwrap());\n tmp.0[2] = 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Otherwise, it'll be zero.\n let is_some = (borrow as u8) & 1;\n\n // Convert to Montgomery form by computing\n // (a.R^0 * R^2) / R = a.R\n tmp *= &R2;\n\n CtOption::new(tmp, Choice::from(is_some))\n }\n\n fn to_repr(&self) -> Self::Repr {\n // Turn into canonical form by computing\n // (a.R) / R = a\n let tmp = Fp::montgomery_reduce(self.0[0], self.0[1], self.0[2], self.0[3], 0, 0, 0, 0);\n\n let mut res = [0; 32];\n res[0..8].copy_from_slice(&tmp.0[0].to_le_bytes());\n res[8..16].copy_from_slice(&tmp.0[1].to_le_bytes());\n res[16..24].copy_from_slice(&tmp.0[2].to_le_bytes());\n res[24..32].copy_from_slice(&tmp.0[3].to_le_bytes());\n\n res\n }\n\n fn is_odd(&self) -> Choice {\n Choice::from(self.to_repr()[0] & 1)\n 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SqrtTableHelpers for Fp {\n fn pow_by_t_minus1_over2(&self) -> Self {\n let sqr = |x: Fp, i: u32| (0..i).fold(x, |x, _| x.square());\n\n let r10 = self.square();\n let r11 = r10 * self;\n let r110 = r11.square();\n let r111 = r110 * self;\n let r1001 = r111 * r10;\n let r1101 = r111 * r110;\n let ra = sqr(*self, 129) * self;\n let rb = sqr(ra, 7) * r1001;\n let rc = sqr(rb, 7) * r1101;\n let rd = sqr(rc, 4) * r11;\n let re = sqr(rd, 6) * r111;\n let rf = sqr(re, 3) * r111;\n let rg = sqr(rf, 10) * r1001;\n let rh = sqr(rg, 5) * r1001;\n let ri = sqr(rh, 4) * r1001;\n let rj = sqr(ri, 3) * r111;\n let rk = sqr(rj, 4) * r1001;\n let rl = sqr(rk, 5) * r11;\n let rm = sqr(rl, 4) * r111;\n let rn = sqr(rm, 4) * r11;\n let ro = sqr(rn, 6) * r1001;\n let rp = sqr(ro, 5) * r1101;\n let rq = sqr(rp, 4) * r11;\n let rr = sqr(rq, 7) * r111;\n let rs = sqr(rr, 3) * r11;\n rs.square() // rt\n }\n\n fn get_lower_32(&self) -> u32 {\n // TODO: don't reduce, just hash the Montgomery form. (Requires rebuilding perfect hash table.)\n let tmp = Fp::montgomery_reduce(self.0[0], self.0[1], self.0[2], self.0[3], 0, 0, 0, 0);\n\n tmp.0[0] as u32\n 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